Shortly after midnight, the hired vehicle swerved into a group of people leaving prayers at the Finsbury Park Mosque, one of the biggest in the country, witnesses said.
The 48-year-old driver of the van was detained by members of the public and then arrested by police on suspicion of attempted murder. No other suspects have been identified as part of the investigation, police said.
Neil Basu, a senior counter terrorism coordinator, told reporters it was too early to say what the motive of the attacker might have been, but that the incident was being treated as a terrorist attack.
"The attack unfolded as a man was already receiving first aid at the scene, sadly that man has died," Mr Basu said.
"Any causative link between his death and the attack will form part of the investigation. It is too early to say if his death was as a result of this attack."
Mr Basu said eight victims were being treated in hospital and two were in a very serious conditions. All were Muslim.
Muslim leaders said worshippers were specifically targeted after leaving prayers and linked the incident to a recent rise in anti-Muslim hate crime.
Witness Abdiqadir Warra told AFP the van "drove at people" and some of the victims were carried for several metres along the road.
London Mayor Sadiq Khan said it was a "horrific terrorist attack," calling it "deliberate" and aimed at "innocent Londoners, many of whom were finishing prayers during the holy month of Ramadan".
May said police had confirmed it was being treated as a potential terrorist attack and said she would chair an emergency response meeting later on Monday.
"All my thoughts are with the victims, their families and the emergency services on the scene," she said.
