By Agence France-Presse
"Serious public security incident under way in Paris in the Louvre area," the interior ministry tweeted as streets in the area were cordoned off to traffic and pedestrians.
The ministry urged people not to spread false information and to follow government accounts for updates.
The shooting comes with France on its highest state of alert with thousands of troops patrolling the streets following a string of attacks in the last few years.
Soldiers in uniform carrying automatic rifles can be regularly seen walking in the area around the Louvre, which is one of the main tourist attractions in Paris, drawing millions of visitors every year.
The huge former royal palace in the heart of the city is home to the Mona Lisa and other world-famous works of art but also a shopping complex and numerous exhibition spaces.
The museum was already suffering from a fall in visitor numbers after recent attacks in France.
Last year, visitor numbers slumped 15 per cent from 2015 to around 7.3 million.
Over the last two years, numbers are down about two million, casting doubt on the Louvre's claim to be the most visited museum in the world.
France has suffered a string of attacks, beginning in January 2015 when jihadist gunmen killed cartoonists and journalists at the offices of the Charlie Hebdo satirical newspaper in Paris in revenge for publishing cartoons of the Prophet Mohammed.
Another attacker went on to kill shoppers in a Jewish supermarket, killing a total of 17 people in three days of bloodshed.
Ten months later, gunmen and suicide bombers from the Islamic State jihadist group attacked bars, restaurants, a concert hall and the national stadium in Paris on November 13, 2015, killing 130 people.
Last July, a Tunisian extremist rammed a lorry through crowds celebrating Bastille Day in Nice on France's south coast, crushing 86 people to death.
And in November, French police broke up an alleged jihadist terror ring which was allegedly planning to attack Paris.