The pedestrian, described as a male possibly in his 40s, was struck by an outbound 21 Hayes bus near Fillmore Street around 10:45 a.m., Sgt. Daryl Fong said.
The man, who witnesses said had stepped out into traffic from between two parked cars, was struck and pinned under the bus.
Officers arriving on the scene performed CPR. The man was transported by ambulance to San Francisco General Hospital, where he was declared dead at 11:15 a.m.
The major accident investigation team and the hit and run detail are investigating the accident, Fong said.
The bus driver has been placed on nondriving status pending an investigation, as is standard procedure, Muni spokesman Paul Rose said.
The pedestrian's identity remains unknown at this time.