The incident occurred at about 7:50 a.m. at Sixth and Mission streets, police spokesman Officer Samson Chan said.
The woman was transported to a hospital with injuries that appeared to be life-threatening, fire department spokeswoman Lt. Mindy Talmadge said.
Police shut down Mission Street between Fifth and Sixth streets to investigate the collision and were talking to the driver, Chan said.
San Francisco Municipal Railway buses were rerouted to Market Street during the closure, Muni spokesman Judson True said. Mission Street reopened at about 9:30 a.m., he said.