Sgt. Dennis Toomer says the incident occurred when the truck was trying to make a right turn in the city's South of Market neighborhood Wednesday morning.
The woman was taken to San Francisco General Hospital where she was pronounced dead from her injuries.
Her name has not been released.
Police say the truck driver has not been cited. His name has not been released.
Police had closed off streets to investigate the crash for about two hours before reopening around 9 a.m.