The BBC reported the attacker inflicted two blows to the officer's head before being shot. A police official would not provide further information.
Large numbers of police cars filled the area on the Ile de Cite island in the Seine River in the centre of Paris as authorities urged people to stay away from the area. Paris police say the situation is now "under control".
Police arrived at the cathedral amid reports of gunshots and panic.
Police in Paris shot and injured a man who tried to attack officers with a hammer at the Notre Dame cathedral.
Others posted photos online of what appeared to be the interior of medieval Notre Dame, one of France's most-visited monuments.
"The police didn't seem interested in him at the beginning", Metreau said. The capital Paris has has a strong police presence on its streets since then. The Paris police department tweeted that one officer was wounded.
Police sources said the officers shot at the man after he had threatened them with a hammer and refused to stop.
Always tight, security in and around the tourist mecca had been stepped up in the wake of recent Islamist attacks on Manchester and London.