The 36-year-old, originally from India but who has lived in the UK for a number of years, was arrested on suspicion of attempted murder and remains in police custody, Derbyshire Police said.
The car, a black Suzuki Swift, struck a number of people in Friar Gate at about 9.30pm on Saturday, police said.
Seven people were taken to hospital with injuries, some of those serious but not life-threatening, Derbyshire Police said in a statement on Facebook.
The statement added: "Derbyshire detectives are leading the investigation with the support of Counter Terrorism Policing colleague.
"Although counter terrorism officers are assisting us with those early investigations, this does not mean the incident is currently being treated as terrorism."
Chief Superintendent Emma Aldred, area commander for Derby, speaking at a media conference, called it a "horrific incident" that has "shocked the city".
Officers were on the scene seconds after a car struck pedestrians, she said.
East Midlands Ambulance Service said it had sent three ambulance cars, seven ambulances and its Hazardous Area Response Team to the scene.
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The ambulance service said it transported seven patients between Royal Derby Hospital and Queen's Medical Centre.
One person who arrived at the scene shortly after the incident told the Derby Telegraph there were "people on the floor".
"It was such a frightening experience. We came around the corner and there was just people everywhere," they said.
"We didn't realise what had happened and then we slowly realised that it was something bad."
A section of Friar Gate is expected to be closed for some time and people are asked to avoid the area.
Baggy Shanker, the MP for Derby South, said his thoughts were with "everyone who has been affected and with their loved ones".
He added: "Thank you to the emergency services for their response. Derbyshire Police have confirmed a man has been arrested and that they do not believe there is an ongoing risk to the public."
Tudor did not win a single one of his five Premier League games, drawing just one, and losing the other four, having replaced Thomas Frank in February.
Spurs said on X: "We can confirm that it has been mutually agreed for head coach Igor Tudor to leave the club with immediate effect.
"Tomislav Rogic and Riccardo Ragnacci have also left their respective roles of goalkeeping coach and physical coach.
"We thank Igor, Tomislav and Riccardo for their efforts during the past six weeks, in which they worked tirelessly."
The club added that "an update on a new head coach will be provided in due course".
His 44 days at the helm now represents one of the shortest managerial tenures in Premier League history.
Only three managers had less time at the top: Sam Allardyce served just 30 days at Leeds in May-June of 2023, Ange Postecoglou had 39 days at Nottingham Forest last autumn, and Les Reed had 40 days at Charlton at the end of 2006.
It comes a week after Tottenham went down to a 3-0 defeat against Nottingham Forest.
Tudor learned of the death of his father, Mario, immediately after the game and was unable to fulfil his post-match commitments.
Recognising his loss, Spurs' statement today said: "We also acknowledge the bereavement that Igor has recently suffered and send our support to him and his family at this difficult time."
With seven games left in its Premier League season, the club is now without a head coach, and just one place and a single point above the relegation zone.
Players not away for international duties will be trained by assistant coach Bruno Saltor in the interim, the Press Association understands.
The side aims to appoint a new head coach in time for its next fixture, on 12 April, against Sunderland.
Among the potential contenders are former Brighton boss, Roberto De Zerbi, and the former manager of Burnley, Everton, and Nottingham Forest, Sean Dyche.
The Tottenham Hotspur Supporters' Trust urged the club to now make a "wise choice" in a post on X, formerly Twitter.
The post called for a manager "we can all be proud of and who can bring some much-needed success and enjoyment to our long-suffering fanbase".
Some held aloft posters of the two well-known Lebanese war correspondents, holding cameras and wearing their press body armour.
A number of women were sobbing. "They're killing the messengers of this war," one said.
Elsy Moufarrej of the Union of Journalists in Lebanon has already described the killings of the journalists as a war crime.
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"We've seen this in Gaza where they tried to undermine Palestinian journalists by linking them to Hamas.
"Now they're trying to do the same to Lebanese journalists by linking them to Hezbollah. Let's be in no doubt. This is a war crime."
The journalists - Ali Shoaib who worked for the Hezbollah-owned TV channel Al-Manar; Fatima Fatouni, who worked for Al Mayadeen; and her brother Muhammad Fatouni, who was a freelance cameraman - were covering the ongoing invasion of Israeli troops inside south Lebanon.
They were travelling together in a vehicle near Jezzine on the highway between Nabatieh and Sidon when an Israeli bomb hit them.
Witnesses said as colleagues ran to help, a second strike hit. The Lebanese health ministry said an ambulance filled with first responders sent to help was also hit.
An Israeli military spokesman admitted they'd targeted the journalists but attempted to justify the killings by claiming one of the senior correspondents - Ali Shoaib - was a member of Hezbollah's elite Radwan force and was passing on information about Israeli troops' movements inside Lebanon.
He provided no evidence for this claim.
The Committee for the Protection of Journalists said journalists doing their jobs are protected under the rules of war, as laid out under the Geneva Convention.
CPJ Regional Director Sara Qudah said: "We have seen a disturbing pattern in this war and in the decades prior of Israel accusing journalists of being active combatants and terrorists without providing credible evidence.
"Journalists are not legitimate targets, regardless of the outlet they work for."
The journalist killings came as Israeli troops intensified their attacks on Lebanon.
Many of these attacks appear to be directed against health facilities and healthcare workers.
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A health care centre in the eastern border town of Deir Kifa was struck early on Sunday.
No one was injured, but the centre has been put out of action.
This was followed by another Israeli attack on an ambulance which had just picked up a casualty.
One paramedic and the patient who'd just been rescued were killed. More than fifty medics have been killed in less than a month.
The Israeli military once again insisted on Sunday that Hezbollah is "using ambulances extensively for military purposes" and continued, "if this practice doesn't stop Israel will act in accordance with international law against military activity".
But the Lebanese health ministry has angrily denounced these claims saying there's no evidence any ambulances are being used for any activity apart from rescuing humanitarian work.
The health ministry is compiling a list of Israeli attacks against health facilities and first responders to present to the UN.
It maintains the Israeli attacks follow a pattern of repetitively targeting medics and hospitals.
"These are war crimes," the health minister Dr Rakan Nassereddine told Sky News.
Lebanon is embroiled in a huge humanitarian crisis caused by the war, with more than a million displaced.
There are daily casualties, with more than fifty killed in the last 24 hours, although the ministry does not differentiate between civilians and combatants.
The Hezbollah militant group continues to fire volleys of rockets into northern Israel.
There has been hand-to-hand fighting between Hezbollah fighters and Israeli troops in some of the southern border villages and communities, but it's difficult to ascertain how much control the Israeli military has of these areas or how much ground they have taken.
There have been sightings of Israeli troops in a number of communities several kilometres inside Lebanese territory and the Israeli Army Chief has been filmed by the military addressing troops on the Lebanese side without any details about exactly where this position was.
Israeli ministers have made it clear their plan is to seize a vast expanse of Lebanon's south in order to create what it calls a 'security buffer zone'.
The government has signalled it intends to occupy this territory right up to the Litani River and potentially beyond (an area which takes up about 10% of Lebanese land) until the Israeli military deems it to be safe from the threat of Hezbollah.
Officers were called to reports of gunshots in Charlton Street, Camden, at 11pm on Saturday.
CCTV footage showed that a man was shot several times while sitting in a white Nissan juke.
Despite paramedics' best efforts, the 26-year-old was pronounced dead at the scene.
Now a search is under way for the killer, who arrived and left on a bike.
The Metropolitan Police have since launched a murder investigation.
Detective Chief Inspector Joanna Yorke, whose team is leading the probe, said: "We are aware of the concern that this will cause for the local community, and want to reassure them that we are working hard to identify the attacker and bring them to justice.
"If anyone has any information that could help us, it is extremely important that they contact the police - either through 101, online or via independent charity Crimestoppers to remain anonymous.
"Our thoughts are with the young man's family at this incredibly difficult time."
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The victim's next-of-kin have been informed and are being supported by specialist officers.
Detained in Dubai chief executive Radha Stirling said she believed dozens of Britons had been arrested in the UAE for sharing war images under the country's "draconian" cybercrime laws.
"We're talking approaching 50 to 70 was my estimate and possibly even more. I think by the end of this we'll see a lot more, possibly 100, maybe 150," she told Sky News.
But the Foreign, Commonwealth and Development Office (FCDO) said it was only providing consular assistance to a "small number" of UK citizens detained over these issues in the Gulf nation.
"We are providing consular assistance to a small number of British nationals detained in the UAE in connection with this issue, and our ambassador is engaging with the Emirati authorities about their cases," an FCDO spokesperson said.
Five Britons are currently receiving consular assistance in the UAE after being detained on such charges, with some already being released, Sky News understands.
Ms Stirling, a human rights advocate and lawyer focused on Dubai, said many Britons had been detained for sharing updates on their welfare, after Iran launched missile and drone attacks against its gulf neighbours in response to US and Israeli strikes.
"Most people did not know and were unaware of these cybercrime laws and the vast extent to which they can be applied, especially in a situation like this," she said.
"There is no way that any of these people knew that it was illegal to send a private message to colleagues saying, 'here I am, I've arrived at the airport. Is it safe for me to walk through, given this explosion', and then sharing a photo of that explosion with colleagues."
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Ms Stirling rejected criticism that Britons who had elected to move to the UAE to take advantage of its tax exemptions were not deserving of government assistance.
"When your citizens are locked up, when they're arbitrarily detained, when they're prosecuted under national security laws for simply sending a photo to a loved one, that's when your government needs to step up," she said.
"And it's irrelevant whether there's tax or no tax in the UAE, our government is obliged to provide that service or else we look weak diplomatically and in the eyes of the world."
Ms Stirling said anyone arrested under cyber security laws could face harsh penalties under the UAE's strict laws, including a life sentence.
"That's expats, that's tourists, some of them for simply sharing a private message saying 'Mum, I'm okay', or to a husband or a wife overseas; 'This building has just been blown up. I live here. Here's a photo of me in my apartment'.
"People are just being arrested, prosecuted or charged and potentially even escalated to national security charges in Abu Dhabi, which could see them in prison for life."