The pedestrians were leaving a nearby hotel in Battersea late on Saturday when the incident happened in Lombard Road.
Police were called at 11.15pm to reports of a fight.
A man in his twenties suffered a broken leg and is in hospital. Another man, also in his twenties, has head injuries but his condition is not yet known.
Two others were also treated in hospital and six others who received minor injuries were treated at the scene.
Police say they are trying to find the driver of the car who fled the scene before they arrived.
The five people arrested are all in police custody and enquiries continue.
Police said the incident was not terrorism-related.