Police said all the victims of the attack were Muslim.
"He has been taken to hospital, and will be taken into custody once discharged", the Metropolitan Police said in a statement.
British security officials, speaking on condition of anonymity in line with official policy, said hate crimes directed at Muslims have increased almost five-fold in the wake of several attacks in Britain.
"This morning we have seen a sickening attempt to destroy those freedoms, and to break those bonds of citizenship that define our United Kingdom", she said.
A man, who was being pinned to the floor by locals, had earlier said "you deserve it" and "I did my bit", eyewitnesses said.
Police said the 48-year-old man who was driving the auto has been arrested and taken to a hospital as a precaution.
The Mayor visits Finsbury Park Mosque along with May and Labour leader Jeremy Corbyn. This is a microcosm of a community working together.
British media have named the suspect in the mosque attack as 47-year-old Darren Osborne, a father of four who was living in Cardiff, Wales. "That's what makes us a strong society and community".
UK moves to ease tensions after London mosque attack
Witnesses reported that the assailant repeatedly said: "I want to kill Muslims". "This person was conscious". Khan also called on Britain's government to supply more funding and resources to the city's police force.
The Leader of the Opposition praised the emergency services for their "very quick and very timely" response after the driver was arrested at the scene. "This is very worrying to the Muslim community".
Later on Monday police insisted that, internally at least, the Finsbury Park incident was treated as a terror attack at 12:29 a.m., a few minutes after officers arrived on the scene. It was not immediately clear why no charge had been made in relation to the one death.
"Diverse, welcoming, vibrant, compassionate, confident and determined never to give in to hate. These are the values that define this country".
Ms Rudd said: "Londoners have been hit with a series of attacks and have actually been nothing short of heroic". Khan replied: "Terrorism is terrorism".
Imam Mohammed Mahmoud was hailed for his efforts to prevent a mob attack and calm the situation before police arrived in shielding the suspected terrorist from the fury of onlookers.
Manchester was also hit by a severe attack when a bomber killed more than 20 people at an Ariana Grande concert. He then used a knife to murder PC Keith Palmer, who was guarding parliament. "The Muslim Community in this area is horrified at this incident and is concerned and shocked at the events".
He added: "I receive briefings from the counter terror team and the good news is the counter terrorism team have been recognizing for a while now there are terrorists motivated by other means other than perverse Islamist motivation".
Neil Basu, the senior national coordinator for counter-terrorism, said: "No matter what the motivation proves to be, and we are keeping an open mind, this is being treated as a terrorist attack and the counter-terrorism command is investigating".
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