"Obviously there is a security system and an alarm in this type of establishment", a police source said.
It is not clear whether any of the loot, estimated to be worth more than €4m (£3.5m), was recovered.
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.
The three arrested men, all around 30 years old, are from the Seine-Saint-Denis area north of Paris, and are "well known to the police for armed robbery, violent crime and receiving stolen goods", a source close to the inquiry said.
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The incident took place at about 6:30 p.m. (1730 GMT) as the streets of Paris were busy with people making their way home from work.
The suspects were wearing gloves and balaclavas and carrying handguns as well as hatchets, according to police sources.
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. The neighbourhood has seen a number of spectacular robberies through the years.
Place Vendome has been the scene of several daring jewellery heists in recent years.
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Three axe-wielding thieves carried out the brazen robbery late on Wednesday at the ultra-chic hotel on the city centre's Place Vendome, next to the Justice Ministry.
On finding their escape route blocked they tried to transfer the loot through a window to two accomplices waiting outside.
Interior Minister Gérard Collomb also offered praise, saying they were "a credit to our police". US reality television star Kim Kardashian was the target of one of the biggest heists in recent years, while attending Paris Fashion Week in October 2016.
Acidente envolvendo 4 veículos deixa 7 mortos e 39 feridos em MG
O acidente foi causado por um caminhão de carga que dirigia na contramão e se chocou contra dois micro-ônibus e uma carreta. De acordo com os bombeiros, uma guarnição de combate a incêndio e duas de salvamento atuam no acidente .