Officers pulled over the suspect's car on Bush Street, about half a block west of Larkin Street, at 1:25 p.m., Suhr told reporters at the scene.
The driver got out of the car and fled, and as two officers chased him, he fired at least two shots at them, Suhr said. Police returned fire, hitting the suspect in the upper body, possibly in the head or neck, the chief said.
The suspect was taken to San Francisco General Hospital, where he is being treated for potentially life-threatening injuries.
A female passenger in the suspect's car slid into the driver's seat and drove away while the officers were chasing the suspect, Suhr said. Police are searching for the car, and believe the passenger is someone known in the neighborhood.
Police have recovered the suspect's gun, and also found an ID on the ground that belongs to a wanted parolee, but do not yet know if the ID is that of the man who was shot.
Larkin Street remained closed between Bush and Sutter streets as of 3 p.m.
Hamood Albadani, 52, who is visiting San Francisco from Michigan, said he witnessed the shooting while walking on Sutter Street.
He said he was at the intersection of Sutter and Larkin streets when he saw a man fire five or six shots toward a parked car, but couldn't see if he was shooting at anything in particular.
He said the shooter was in the street, and that a police officer approached him from the sidewalk and fired one shot to the man's head, taking him down.