Two further suspects are being sought by police.
Police say they have recovered the millions of dollars worth of jewels that were snatched from glass display cases and caught three robbers who got blocked inside the premises.
The robbery on Wednesday evening saw a gang armed with hatchets and handguns burst into the hotel on the capital's glitzy Place Vendome and smash the display windows of jewellery shops on the ground floor.
A police team in charge of patrolling the square - home to some of Paris's top jewellers and watchmakers, as well as the Justice Ministry - was quickly on the scene.
It was at the Ritz that Diana, Princess of Wales, spent her last night in 1997 before the vehicle crash that killed her and her lover Dodi Fayed, al-Fayed's son. Two accomplices waiting outside were thrown some booty and escaped by auto and motorbike.
The hotel, opened in 1898, has been owned by Egyptian billionaire Mohamed Al-Fayed since 1979.
The getaway vehicle was found about 20 kms (12 miles) north of Paris in an area where the three arrested came from.
Place Vendome has been the scene of several daring jewellery heists in recent years.
The other made a getaway on a motorbike, dropping a bag of jewels and knocking over a pedestrian while speeding the wrong way up a one-way street.
Interior Minister Gérard Collomb also offered praise, saying they were "a credit to our police".
But the audacious strike at one of Paris's most glamorous hotels could cast a cloud over the Ritz's image.
France has found itself repeatedly in the headlines for high-profile robberies, particularly in Paris and on the Cote d'Azur.
In December, a man was able to substitute two diamonds and two rings worth 5.5 million euros in a jewellery store replacing them with fakes.