The heavy-rescue squad had its siren on and was en route to a one-alarm fire in the Sunset District around 1:30 p.m. when it collided with a Ford Mustang at a four-way stop, fire Lt. Mindy Talmadge said.
The Mustang then struck a silver Toyota Tacoma that had pulled over to get out of the way of the fire truck.
Two occupants of the Mustang were extricated and taken to a hospital to be treated for injuries that were not considered life-threatening, Talmadge said.
There were no other reports of injuries.
Talmadge said the firefighters had been responding to a fire at 1114 Judah St. Another truck took over the call and the fire has since been controlled.
The fire injured an elderly woman, who was taken to a hospital for treatment, Talmadge said.
The cause of the collision is under investigation.