The incident just after 9 p.m. Monday left the victim, 60, with life-threatening injuries.
Detectives are calling witnesses to the Vesta Road collision, Brockley, to report.
The driver of the black SUV did not stop on the spot and the injured man remains in hospital.
Police said they searched CCTV footage to put together how the man sustained such serious injuries.
They also want drivers who potentially have dahscam footage to report.
Detective Louise Woodgate, of the Serious Collision Investigation Unit, said: “We are very eager to speak with everyone who was in the Vesta Road area at the time and saw the collision or the moments that led up to it.
“We will also ask everyone in the area to check their CCTV or dashcam footage and contact us as soon as possible if you find anything that can help our queries.”
Anyone with information should call 020 8285 1574 with CAD 7336 / 1NOV.