The collision was reported at 1:23 p.m. near the corner of Larkin and Jackson streets, police said.
The vehicle was traveling west on Jackson Street when the driver, who works for the transportation network company Lyft, made a left turn onto Larkin Street and hit a woman who was walking in the crosswalk, police said.
The woman was taken to San Francisco General Hospital with a leg injury. Her injuries were not life-threatening, police said.
Lyft representatives confirmed this evening that the driver was carrying a Lyft passenger at the time of the crash. The company said the driver alerted them to the collision and that the driver was deactivated as the company collects more details.