A man, 48, has been arrested in connection with the incident.
Police said a suspect was quickly and calmly turned over to the police, and that no one else was found in the van.
Video posted on social media showed people screaming as bystanders performed chest compressions on one of the injured.
Another witness, Abdikadar Warfa, said: "I saw a man underneath the van".
Opposition Labour Leader Jeremy Corbyn said he was "totally shocked ... by the terrible event". Vehicles have also been also used to attack the public on London's Westminster Bride, in Nice, and in Berlin.
Mohammed Kozbar, chairman of the Finsbury Park Mosque, called the incident a "cowardly attack" on worshippers.
He described it as a terrorist attack condemning the incident. People are reporting of several injured, some fatalities.
Finsbury Park mosque was once a notorious hub for radical Islamists but has entirely changed in recent years under new management. Police said they've not identified any other suspects at the scene nor have any been reported to police.
The crash occurred near the Finsbury Park mosque.
Sadiq Khan, Mayor of London, has urged people to "remain calm and vigilant".
Today's incident followed a series of attacks in Britain.
Reuters quoted an eye witness as saying that he saw at least one person being loaded into an ambulance. He has been taken to a hospital for an evaluation, and will be placed in police custody immediately upon his discharge.
Someone in the crowd is heard shouting, "No one touch him! No one! No one!"
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There is also no rule barring such donations, said David Alan Sklansky, a criminal procedure professor at Stanford University. If the dominos continue to fall, one of five assistant attorneys general or the solicitor general would assume the role.
Both Muslim Welfare House and the Finsbury Park Mosque are a short walk south of Finsbury Park train station.
Several worshippers were in the area at the time of incident after attending Ramzan prayers.
Police said the incident took place near Finsbury Park Mosque in Seven Sisters Road.
The council clarified that the incident took place outside the Muslim Welfare House, 300 meters away from the mosque.
The group's secretary general, Harun Khan, said in a statement that eyewitness accounts suggest "the perpetrator was motivated by Islamophobia". Two others were treated on the site for minor injuries.
"We don't yet know the full details, but this was clearly a deliberate attack on innocent Londoners, many of whom were finishing prayers during the holy month of Ramadan".
Britain's terrorist alert has been set at "severe" meaning an attack is highly likely. The van driver tried to escape but people grabbed him.
Earlier this month, three knife-wielding Islamist attackers went on a rampage in the British capital, plowing a van into pedestrians on the London Bridge before stabbing revellers in a nearby market, killing seven people.
He said: "When I drove past slowly I could count three people on the floor and police were performing CPR on one of them".
"He will also be subject of a mental health assessment in due course".
During the 2016 USA presidential campaign - amid the furor of candidate Donald Trump's proposed Muslim ban - Labour Party leader Jeremy Corbyn invited Trump to visit Finsbury Park Mosque to show him how "multicultural, multifaith" Britain works.
The Muslim Council says a van has "run over worshippers" leaving the Finsbury Park mosque.
During Ramadan - the name of the ninth month in the Islamic calendar and the holiest time of their year - Muslims fast daily from dawn to dusk and focus on prayer, purification and acts of charity.
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