Officers were dispatched to Lewis and Senter roads around 12:35 p.m. after receiving a report of a knife-armed man. Police released no further information about the shooting.
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The man is being treated for his injuries at a hospital, police said. The officer, who has not been named, has been placed on paid leave.
The Santa Clara County District Attorney's Office and the police department are investigating the shooting. The police Internal Affairs Unit, the City Attorney's Office and the Office of the Independent Police Auditor are monitoring the case.
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Anyone with information about this incident has been asked to call San Jose police Detective Sgt. Michael Montonye or Detective Jason Tanner at (408) 277-5283.