The attacker is said to have been trying to enter the museum, which was evacuated soon after.
He is thought to have been carrying either one or two suitcases.
A big security operation is now reported to be under way at the Louvre and a nearby shopping centre in the French capital.
French police have said the attacker shouted “Allahu Akbar” – which means ‘God is great’ in Arabic – but was not carrying explosives.
Meanwhile, the British Foreign and Commonwealth Office has updated its French travel advice.
A spokesman for the FCO said: “There are reports of a security incident in the area around the Louvre museum in Paris; you should exercise caution, avoid the affected area and follow the advice of the local authorities.”