Police were called by the London Ambulance Service at 3.09pm on Monday, 14 September to reports of a collision between a car and pedestrian on Victoria Road, Surbiton.
The man, aged 29, was taken to a south London hospital where his condition was later assessed as non life-threatening.
The driver of the car involved did not stop at the scene and the vehicle was found abandoned a short time later further down the same road.
Detective Inspector Andy Griffin, from South West CID, said: “We have spoken to a number of people at the scene, but we know there are others who saw the incident, or the immediate aftermath, and have not yet spoken to police.
“We would urge any witnesses, or anyone who believes they may have any information, to come forward and speak to us. Additionally, we would ask anyone with a dashcam who was in the area at the time, to check whether they inadvertently captured anything that could help our investigation.”
Anyone with information should call 101 with reference number 4360/14Sep. Alternatively contact Crimestoppers anonymously on 0800 555 111.
A man, aged in his 20s, attended a south London police station later on Monday, 14 September. He was arrested on suspicion of dangerous driving and failing to stop at the scene of an accident.
He has been released on bail to a date in October.