The attack comes during the Muslim holy month of Ramadan, when people attend prayers at night.
Two worshippers were feared killed, according to the Sun newspaper, but there was no immediate confirmation of this.
Prime Minister Theresa May said her thoughts were with those injured in "this terrible incident". The leader of the opposition Labour Party, Jeremy Corbyn, said he was "totally shocked".
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 the city. They said there were a number of casualties and one person had been arrested.
"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'," one woman who lives opposite the scene told the BBC.
"There was this white van stopped outside Finsbury Park mosque that seemed to have hit people who were coming out after prayers had finished.Read more at Reuters