The shooting occurred in the 1400 block of Gage Avenue in Florence around 10 p.m.
Deputies were reportedly in pursuit of a possible reckless driver, under the influence of alcohol or drugs, when a passenger in the suspect's vehicle jumped from the car and ran.
"Meanwhile, other deputies continued to pursue the driver of the fleeing vehicle," a department statement said. "Eventually, the driver yielded and was taken into custody after a brief struggle with deputies."
The suspect who fled on foot was wounded and transported to a local hospital with non-life threatening injuries.
No deputies were injured.
Officials said a handgun was recovered at the scene.
A large area was blocked off to traffic during the investigation. A Metro bus was forced to make a U-turn and accidentally took out a fire hydrant. That mess was cleaned up Sunday morning.
CNS contributed to this report.