The van driver, described by eyewitnesses as a large white man, was detained by members of the public after the attack in Seven Sisters Road at 12.20am on Monday.
One witness described being surrounded by bodies in the wake of the attack outside the Muslim Welfare House, close to Finsbury Park mosque.
Another said the attacker shouted about killing Muslims as he was held by local people.
The Metropolitan Police said in a statement: "One man was pronounced dead at the scene.
"Officers are in the process of informing next of kin. A post mortem examination will be scheduled due course.
"Eight people injured were taken to three separate hospitals; two people were treated at the scene for minor injuries."
Commenting on reports that the van driver also produced a knife, the statement went on: "At this stage there are no reports of any persons having suffered any knife injuries.
"The driver of the van - a man aged 48 - was found detained by members of public at the scene and then arrested by police in connection with the incident.
"He has been taken to hospital as a precaution and will be taken into custody once discharged.
"He will also be subject of a mental health assessment in due course."
The force said the investigation of the incident is being carried out by the Counter Terrorism Command.
Some witnesses at the scene said more than one attacker may have been involved.
But the Met said: "At this early stage of this investigation, no other suspects at the scene have been identified or reported to police, however the investigation continues."
The force added: "Due to the nature of this incident extra policing resources have been deployed in order to reassure communities, especially those observing Ramadan."
Prime Minister Theresa May said: "Police have confirmed this is being treated as a potential terrorist attack.
"I will chair an emergency meeting later this morning.
"All my thoughts are with the victims, their families and the emergency services on the scene."
Our hearts, thoughts and prayers are with all those affected by the #FinsburyPark van attack.
— The Methodist Church (@MethodistGB) June 19, 2017
Once again terrible news: praying for an end to the evil and the triumph of good. Our hearts go out to all those affected. #WeStandTogether
— Luke Miller (@ArchdeaconLuke) June 19, 2017
Waking to another act of terror, this time not far from where we live. Lord have mercy on us
— Fr Christopher (@revdchris) June 19, 2017
Dear Lord,
— krish kandiah (@krishk) June 19, 2017
Please console the mourners,
Comfort the injured,
Equip the investigators &
Heal our nation. #FinsburyParkattack
