People have been told to stay away from the area, which is one of the French capital's most popular tourist sites.
Reports suggest a man attacked a police officer with a hammer and was later shot.
Police in Paris say a security operation is under way near the Notre-Dame Cathedral and people are urged to stay away from the scene.
No specific details were given about the incident in a tweet by police.
Large numbers of police cars sped to the area on the Ile de Cite island in the River Seine.