A spokesman for the military force that patrols key sites in Paris says a four-man patrol of soldiers attacked at the Louvre tried to fight off an assailant before they opened fire.
Spokesman Benoit Brulon says a soldier who was slightly injured by the attacker was not the solider who opened fire.
France's Interior Ministry said that the man's identity or nationality were currently unknown. It added that he was alive after the shooting, but there have been no further updates on his condition.
Anti-terrorism prosecutors have opened an investigation into the incident, which took place in an underground shopping mall close to the historic museum.
Police said that a second person who was behaving suspiciously had been arrested. Police officials said the individual did not appear to be connected to the attack, but that prosecutors would determine if they were involved.
Interior Ministry spokesman Pierre-Henry Brandet told the Associated Press that around 1,000 people were held inside secure areas of the museum during the incident for their own safety.
Authorities said they would be released in small groups once they had been vetted.
Interior Minister Bruno Le Roux said that he "salutes the composure and professionalism of the military and police," in a statement released via Twitter.
Agencies reported that staff were returning to the shops in the mall where the shooting took place by around 12:30 p.m. local time (06:30 a.m. ET), and that roadblocks had been cleared from the surrounding area.
France has been under a state of emergency since the 2015 terrorist attacks in Paris that killed 130 people.
Soldiers on patrol are part of security measures that have beefed-up in the wake of attacks in the capital and in Nice.
The museum is one of central Paris' biggest tourist attractions and is one of the most-visited museums in the world.