Lt. Steve Prendergast says the suspect and the bystander were hurt around 1 p.m. Wednesday in downtown Los Angeles.
At least two officers chased the stolen vehicle in their patrol car for about 10 minutes before chasing a male suspect on foot.
Prendergast says the incident is under investigation and it's unclear why officers drew their weapons or opened fire.
He says the Los Angeles County Sheriff's Department will conduct the investigation.
The officers have been given time off following the incident, but are not suspended. They were not injured.
Prendergast gave no details on the severity of the injuries.