It happened in the area of Ellis and Geary streets Friday at about 10:50 a.m.
Three large dogs reportedly began attacking a smaller dog and a pedestrian.
The owner of the smaller dog then left the scene to get care for his dog, police say.
Crews arrived on the scene and found one person -- the second pedestrian -- was bitten in the attack. That person was transported to the hospital in stable condition.
SFPD and animal control officials secured the dogs, one of which was shot and killed. Another was taken into custody. Officers followed a third, which was taken into custody after it was shot and injured.
The three dogs appear to all be adult dogs, and animal control officials are working to identify the breed.
The small dog that was attacked is being treated for injuries.
This is a breaking news story. Check back for updates.