One person was arrested following the incident on Seven Sisters Road.
Officers were called at 00.20 BST and remain at the scene, the Metropolitan Police said, describing it as a "major incident".
The Muslim Council of Britain (MCB) said a van "intentionally" ran over people.
Witnesses said the area was busy because worshippers had been attending evening prayers.
London Ambulance Service said it had sent "a number of resources" to the scene.
One eyewitness who lives in a flat on Seven Sisters Road told the BBC she saw people "shouting and screaming".
"Everyone was shouting 'a van's hit people'.
"There was this white van stopped outside Finsbury Park Mosque that seems to have hit people who were coming out of the mosque after prayers finished."
She said the road was "backed up" with police cars, ambulance and fire engines.
Others have described seeing police tend to the injured.
Cynthia Vanzella said on Twitter: "Horrible to watch police officers doing cardiac massage at people on the floor, desperately trying to save them. I just hope they did."
The MCB said its "prayers are with the victims."