The 48-year-old driver was arrested by the police.
The London Ambulance Service said eight people were taken to hospital and a number of people were treated at the scene for minor injuries.
Meanwhile, Prime Minister Theresa May has said the police were treating the van incident "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," The Telegraph quoted May, as saying.
Earlier, she had described it as a "terrible incident", adding, "All my thoughts are with those who have been injured, their loved ones and the emergency services on the scene," The Guardian had quoted her, as saying.
London mayor Sadiq Khan called it a "horrific terrorist attack."
"While this appears to be an attack on a particular community, like the terrible attacks in Manchester, Westminster and London Bridge it is also an assault on all our shared values of tolerance, freedom and respect.
The situation is still unfolding and I urge all Londoners to remain calm and vigilant," The Telegraph quoted him, as saying.
The attack came shortly after worshippers attended evening prayers at the Muslim Welfare House.
The incident follows a series of attacks in Britain. Eight people were killed and 50 injured on June 3 when three terrorists drove into pedestrians on the London Bridge and stabbed people at nearby restaurants and bars in the Borough market.
Two weeks earlier, a suicide bomber killed 22 people at a concert by American pop singer Ariana Grande in Manchester in northern England.
On March 22, a man drove a car into pedestrians on the Westminster Bridge in London and stabbed a policeman to death before being shot dead killing five people.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)