Five men armed with axes smashed a window at the shop inside the hotel at about 18:00 local time (19:00 GMT), French media report.
Three men have been arrested, police said, while others remain on the run.
It is not clear whether any of the loot, estimated to be worth more than €4m (£3.5m), was recovered.
The luxurious five-star Ritz is located in Place Vendôme, in Paris' historical first district on the right bank of the river Seine. The ministry of justice lies next door.