The van struck people after mounting the pavement just after midnight BST outside Muslim Welfare House, near Finsbury Park Mosque. A 48-year-old man has been arrested.
Home Secretary Amber Rudd said police were treating it as a “terrorist incident”.
Eyewitness Abdul Rahman said the driver said he wanted to “kill all Muslims”.
Mr Rahman told the BBC he struck the man and helped subdue him.
“When the guy came out from his van he wanted to escape, run away and he was saying ‘I want to kill Muslims. ‘I want to kill Muslims.’
“I hit him on his stomach… and then me and the other guys… we held him to the ground until he couldn’t move. We stopped him until the police came.”
Counter-terrorism officers are at the scene, the Metropolitan Police said.
And extra police are being deployed to reassure communities, especially those observing Ramadan, Mayor of London Sadiq Khan said.
He also said his “thoughts and prayers” were with those affected by the “horrific terrorist attack on innocent people”.
“While this appears to be an attack on a particular community, like the terrible attacks in Manchester, Westminster and London Bridge it is also an assault on all our shared values of tolerance, freedom, and respect.”
Metropolitan Police’s deputy assistant commissioner Neil Basu said the attack began when the van was driven into a man who was already being given first aid by the public on the pavement.
“Sadly that man has died. It is too early to state if his death was a result of this attack.”
All the victims were Muslim and there are currently no other suspects, he added.
The 48-year-old man has been arrested on suspicion of attempted murder.
Harun Khan, secretary general of the Muslim Council of Britain said: “Over the past weeks and months, Muslims have endured many incidents of Islamophobia, and this is the most violent manifestation to date.
“We expect the authorities to increase security outside mosques as a matter of urgency.”
Many of the victims are believed to have just left evening prayers at the Muslim Welfare House after breaking the Ramadan fast.
It has appealed for calm, adding that “all of our efforts should be towards getting justice for the victims and ensuring our community stays the diverse, tolerant and welcome place we know it to be”.
The prime minister will chair a meeting of the emergency Cobra committee later.
Mrs May described it as a “terrible incident”, adding: “All my thoughts are with those who have been injured, their loved ones and the emergency services on the scene.”