The Royal Tenenbaums star lost his temper after a man, identified by TMZ.com editors as Bruce Becker, approached Hackman and his wife Betsy Arakawa in an aggressive manner outside a restaurant in Santa Fe, New Mexico.
Police Sgt. Andrea Dobyns confirms the 82-year-old star lashed out and smacked Becker across the face after he called Arakawa a derogatory name and made the couple fear for their safety.
Becker reported the incident to cops, who interviewed Hackman and Arakawa and determined the slap was made in self-defence. No charges were filed.
Dobyns tells EOnline.com, "(The hit was) more like a slap than a punch. It looked like Mr. Hackman did this purely out of self-defence to protect himself and his wife."