The woman was headed east on Mission Street and was hit by the westbound truck as she turned left onto Fremont Street just after 8 a.m., police Lt. Troy Dangerfield said.
Both the truck driver and the bicyclist had a green light, but the bicyclist was making an illegal left turn, Dangerfield said.
Signs posted at that intersection only permit left turns for taxis and San Francisco Municipal Transportation Agency buses.
The woman, who was not wearing a helmet, suffered a serious head injury along with injuries to her body and was taken to San Francisco General Hospital, he said.
Police have obtained footage of the accident from a video camera at a nearby business, Dangerfield said.
The driver of the truck, owned by the Newark-based company Sunrise Food Distributors Inc., cooperated with investigators, and drugs and alcohol are not believed to be factors in the collision, he said.
Dangerfield said he estimates that the intersection would be closed until at least 11 a.m.
He said the collision should serve as a warning for bicyclists, motorists and pedestrians.
"Everyone has to share the roadway and be cautious," Dangerfield said.