The hotel is located beside the French Justice Ministry which is guarded by armed soldiers around the clock.
A witness told Sky News they heard "at least 10 rounds of gunfire".
Police are now hunting the rest of the gang who managed to escape.
The five bandits broke glass showcases to steal jewellery and precious stones on display at a shop inside the hotel, which stands on the upmarket Place Vendome in the French capital.
Three suspects have been detained and two others are on the run, the source said.
Other guests cowered on the floor of the hotel's Hemingway bar during the raid, which happened around 6.30pm yesterday.
'Bar staff told everybody to remain calm, and not to do anything stupid.
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Paris police commissioner tweeted a statement thanking the officers for their quick reactions.
On finding their escape route blocked they tried to transfer the loot through a window to two accomplices waiting outside.
2 employees who were in the shop during the robbery were apparently not injured.
The five-star residence, owned by Mohamed Al-Fayed, is no stranger to controversy.
But when police arrested two suspects at scene, "it soon became clear that it was a robbery", the source added.
The Ritz was founded by Swiss hotelier César Ritz in 1898 and has been a focus of high society ever since. It was the last place Princess Diana stayed before her fatal auto crash and hosts elite guests from around the world who prize the refined neighborhood.
The luxurious Ritz is in Paris' First Arrondissement, a district located principally on the Right Bank of the Seine River, and includes five shops and almost 100 "showcases" that sell jewelry and luxury goods, BBC reported.