The man injured the face of an officer at the entrance to the police station in Joue-les-Tours near the city of Tours in central France and injured two other before he was shot, the interior ministry said.
Anti-terrorist investigators were probing the incident, a judicial source said.
The perpetrator was a French citizen born in Burundi in 1994 and known to police for common crimes, a source close to the case told AFP.
Officials said the condition of the three wounded police officers was stable.