The collision was reported at about 3:45 a.m. in the 400 block of Hyde Street.
The vehicle and the bicyclist, who is in his mid 20s, were both traveling south on Hyde Street approaching Ellis Street, police spokesman Sgt. Dennis Toomer said.
The bicyclist apparently does not remember if the vehicle struck him or if he struck the car, but other people in the area heard a loud noise and then saw the bicyclist on the ground, Toomer said.
He was taken to San Francisco General Hospital to be treated for his injuries, which are not considered life-threatening, according to Toomer.
Investigators have not found any witnesses to the collision and are looking for surveillance video footage that may shed more light on the case, Toomer said.
The vehicle involved in the collision has been described as a white, four-door sedan, police said.
Anyone with information about the case is encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or to send a tip by text message to TIP411 with "SFPD" in the message.