One man was pronounced dead at the scene of the attack in the early hours of Monday morning, a police statement said, adding that a 48-year-old suspect had been arrested.
"The driver of the van...was found detained by members of the public at the scene and then arrested by police in connection with the incident," the statement said. Ambulance crews said ten people had been transferred to hospital.
"Police have confirmed this is being treated as a potential terrorist attack," Prime Minister Theresa May said, adding she would chair an emergency meeting later this morning.
"All my thoughts are with the victims, their families and the emergency services on the scene," she said.
According to Home Secretary Amber Rudd the Metropolitan Police confirmed the incident was being investigated by its Counter Terrorism Command Unit.
"We must all continue to stand together, resolute, against all those who try to divide us and spread hate and fear," Rudd said.
As it happened
Police said they were called just after 12:20 a.m. (2320 GMT Sunday) to reports of a collision on Seven Sisters Road, which runs through the Finsbury Park area of north London.
A witness who lives opposite the scene told the BBC a white van stopped near the Finsbury Park mosque, as Muslims celebrated Ramadan in the multi-ethnic area.
"From the window, I started hearing a lot of yelling and screeching, a lot of chaos outside…Everybody was shouting: 'A van's hit people, a van's hit people'," she said. "I didn't see the attacker himself, although he seems to have been arrested, but I did see the van."

The UK's largest Muslim umbrella body, the Muslim Council of Britain (MCB), said on Twitter that the crash happened outside the Muslim Welfare House, just down the road from Finsbury Park mosque. "Our prayers are with the victims," it said.
At least two witnesses told Sky News there were three men in the van, but the police statement seems to contradict that, saying no other suspects had been identified or reported to police.
Harun Khan, the head of the MCB, described the incident as the "most violent manifestation to date" of Islamophobia, and called on authorities to do more "to tackle the growth in hate crime."
"Terror Attack" on Worshippers Leaving #FinsburyPark @MuslimCouncil statement: https://t.co/afA3zNBHq7 pic.twitter.com/BYqxfWQaJu
— MCB (@MuslimCouncil) 19 June 2017
UK on high alert
London is on edge after eight people were killed in a van and knife attack on London Bridge and the Borough Market area earlier this month. In March, a man drove a car into pedestrians on Westminster Bridge and stabbed a police officer to death before being shot dead. In May, the city of Manchester was targeted with a suicide bombing at a pop concert that killed 22 people.
Britain's terrorist alert has been set at "severe," meaning an attack is highly likely.
Police said they had deployed extra policing resources "to reassure communities, especially those observing Ramadan."

Finsbury Park: hotbed of radical Islam
The Finsbury Park mosque has been associated with radical Islamist ideology in the past, but its image changed after it was shut down and reopened under new management.
Its former imam, Abu Hamza, was jailed in Britain for inciting violence and racial hatred before being extradited to New York, where he was sentenced to life in prison for terrorism in 2015. That same year, the mosque took part in an open day organized by the MCB to promote better understanding of Islam following Islamist-inspired attacks in Paris. It has not been associated with extremist views for more than a decade.