He was standing outside a stationary police vehicle which was damaged by the smash in Camden, north London.
The driver did not stop at the scene following the crash in Dartmouth Park Hill just before 3pm on Thursday.
Medics took the policeman to hospital suffering from lower body injuries which are not life-threatening.
Both the motorist and vehicle are still being sought, a police spokesman said.
Ken Marsh, chairman of the Met Police Federation representing rank-and-file officers, said: “My thoughts go out to this colleague as he recovers.
“Yet again an officer has been injured simply doing their job. This is what happens in London on a daily basis.”
Anyone who saw the incident, has dashcam or moving footage can call the police on 101 or tweet @MetCC quoting 4030/15APR.
Anyone who wants to stay anonymous can call Crimestoppers on 0800 555 111 or visitCrimestoppers-uk.org, the police said.