The collision was reported at 4:04 p.m. near Fifth and Bryant streets.
The 38-year-old bicyclist was riding behind a vehicle heading north on Fifth Street, and rode into the rear of the car when it stopped, according to police.
The man suffered life-threatening head injuries and was taken to San Francisco General Hospital, police said.
No other information about the accident was immediately available Thursday evening.
Cycling advocates have called on San Francisco to increase safety measures in SoMa neighborhood, where all four of the bicyclist fatalities in The City this year have occurred.