The man, who tried to gain entry to the Louvre's shopping centre, was shot in the abdomen and seriously injured.
President Francois Hollande said the situation was under control but the "threat of terrorism is here to stay".
The Louvre is home to numerous celebrated art works, including the Mona Lisa.
It is due to reopen on Saturday, according to French Culture Minister Audrey Azoulay.
The incident began at 10:00 local time (09:00 GMT) in the Carrousel du Louvre shopping centre at stairs leading to an entrance to the museum itself.
A patrol of four soldiers are reported to have tried to subdue the assailant using non-lethal force after he rushed at them.

When this failed and after one soldier was injured, five shots were fired. The suspected attacker was taken to hospital.
An image circulating in French media, said to have been taken by a tour guide, shows what is believed to be the suspect lying at the foot of the stairs, surrounded by armed soldiers.
Two rucksacks belonging to the suspect, who shouted "God is greatest" in Arabic, have been inspected but no explosives were found.
There were reports of a second arrest, but the prosecutor's office later told the BBC this was not the case.