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7 year oldThe 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.
Little is known about the main suspect, who is reported to be in his 30s and without identity papers.
President Hollande praised the soldiers' actions, saying "this operation prevented an attack whose terrorist nature leaves little doubt".
He told reporters at an EU summit in Malta on Friday that he expected the suspect to be questioned "when it is possible to do so".
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Hundreds of visitors in the Louvre at the time were held in secure areas of the museum, before they were evacuated gradually after security checks.
As the attack unfolded, they were told by security staff to crouch on the floor.
Witnesses described scenes of panic.
One woman, who works at a restaurant in the Louvre, told the AFP news agency: "We saw death coming for us, with everything that's happening at the moment. We were very, very scared."
France has been on a high state of alert since the Paris attacks of 2015. Thousands of troops on the streets form part of the stepped-up response.
A series of assaults by gunmen and suicide bombers claimed by so-called Islamic State killed 130 people in November 2015.
In January of the same year, 17 people were killed in an attack on the Charlie Hebdo magazine and linked shootings.
Last July, 86 people were killed when a lorry ploughed through crowds celebrating Bastille Day in Nice.
Security has become a theme of the French presidential election in April, which sees far-right leader Marine Le Pen and centrist independent Emmanuel Macron leading the polls.
Though still hugely popular, the Louvre has suffered a drop in visitor numbers amid fears of a militant attack.
It was ranked as the world's most visited museum in 2015 but there are doubts whether it still holds the top spot.
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