The condition of those injured in the crash, which happened in Battersea at about 10:30 GMT, has not been confirmed. Road closures are in place.
Four ambulance crews were sent to the scene, near the junction of Kirtling Street and Battersea Park Road, along with the air ambulance.
The car's 35 year-old driver has been arrested on suspicion of causing serious injury by dangerous driving.
Seven people were treated in hospital following the crash. Five people were treated for minor injuries while two remain in hospital. Their condition is unclear.
In a statement the London Ambulance Service said: "We sent a paramedic on a motorcycle, four ambulance crews, an advanced paramedic and an incident response officer to the scene alongside our hazardous area response team. London's Air Ambulance was also dispatched.
"We treated six patients at the scene and took them to hospital."
Six people were injured when a Ferrari 458 Speciale hit them in south London.