The officer was shot after encountering two suspects at a community centre who fired at him during a foot chase, police say.
County Police Chief Jon Belmar says the officer was shot in the arm and is expected to survive but did not give further details about his condition.
He says the officer fired shots in return but police have no indication that either suspect was shot.
A search was underway for the suspects early on Sunday.
Belmar says he does not think the shooting was related to two separate protests that were going on Saturday night around the same time.
The city has been the scene of unrest since the August 9 shooting of Michael Brown, an unarmed, black 18-year-old, by a white police officer.
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