Scotland Yard said four teenagers armed with knives have been arrested in connection with the incident, which is not being treated as "terrorist related".
"Police were called to reports of a car in collision with a number of people. Officers and London Ambulance Service attended the scene. Three people - two males and one female - were taken to hospital for treatment to their injuries, Metropolitan Police said.
"The occupants decamped from the car and fled the scene on foot. Four males, aged between 17 and 19, have since been arrested on suspicion of a variety of offences including GBH [grievous bodily harm] with intent and possession of points and blades. All four remain in custody," it said.
"This is not being treated as terrorist related," the Metropolitan Police Service statement added.
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Eyewitnesses took to Twitter to describe the carnage left by the car after it mounted the pavement.
Jade Barlow wrote: "It's all kicking off on Essex road, Islington... A handful of casualties and a very large knife... hmmm. An abandoned knife and a handful of mowed down casualties."
The incident comes just days after terror suspect Khalid Masood had on Wednesday driven a car at high speed down Westminster Bridge in London before attempting an attack on the Parliament, killing four people and injuring 50.