Police were still trying to find two of the gang on Thursday, although officers patrolling the area detained three of the thieves at the scene.
They had entered the hotel by the rear entry wearing masks and armed with hatchets and handguns at about 6.30pm, smashed the windows and passed the booty to their accomplices outside the front of the hotel.
They were caught as they tried to leave by the rear doors, which had already been closed.
Some of the stolen goods, estimated to be worth more than four million euros, was found dropped in the street at the time of their arrest.
One of the robbers who managed to get away also dropped a bag containing jewellery and watches, a police source told the AFP news agency.
Interior minister Gérard Collomb praised officers' "professionalism", saying they had "done our police force credit".
History of heists
Luxury brands display their products in the Ritz's street-front windows.
Security was stepped up in the area, home to France's justice ministry as well as to a number of luxury-goods shops, in 2014 after several armed raids in which jewels worth between 420,000 and two million euros were stolen.
In 2016 an estimated jewellery worth an estimated six million euros was stolen from fashion brand Chopard.
Also in 2016 thieves stole jewellery worth about nine million euros from US reality TV star Kim Kardashian.