Ambulances were called to the scene, rushing one man aged in his 50s to hospital with serious leg injuries and transporting two others with minor injuries for further treatment.
Hassan Naddi, head of security for The Hussaini Association, said taunts of "dirty Muslims" could be heard coming from the auto, which contained three men and one woman.
A spokesman for the Hussaini Association, who were running the Al Hussaini Majis commemorating an Islamic prophet, claimed the incident was a "deliberate Islamophobic attack" and said they were in "deep shock".
No arrests have been made.
Police were "retaining an open mind regarding the cause of the collision".
Scotland Yard added they were not treating the incident as a terror-related but added 'the hate crime aspect of the collision is being looked at by detectives as an aggravating factor'.
The three men and a woman in their mid-20s were then involved in a row with a group outside the centre where anti-Muslim language was apparently used.
The two hospitalised people are not believed to have life-threatening injuries, the police said.
It's alleged Islamophobic comments were made by those in the vehicle.
After asking the individuals, described as being in their mid-20s, to leave, a confrontation took place between the occupants and "a large group of people visiting the centre".
In a statement posted on social media, the association said a red Nissan Juke "swerved into innocent bystanders, hitting at least five people of which three were seriously injured".
Officials said some anti-Muslim comments were made and the vehicle reportedly sustained minor damage from some of the people from the centre. If you were there at the time and have information I would urge you to contact police with information.