The accident happened shortly before 8:40 a.m. on Market Street near Fifth Street.
Muni spokesman Judson True said the bicyclist may have fallen into the path of the inbound 5-Fulton bus. It appears the front of the bike was run over by the rear wheels of the bus, he said.
The bus driver didn't stop right away and Muni is investigating why.
"Clearly, a Muni operator who is informed of a collision should stop immediately and call central control," True said.
The bicyclist was taken to San Francisco hospital with injuries that were not life-threatening, he said.