Reports say the suspects, who are known to police for previous burglaries, were arrested on Saturday evening.
Specialist police have now taken on the case and can question them for up to 96 hours.
In a statement, the Paris prosecutor’s office criticised the “premature disclosure” of information related to the case, adding it hindered efforts to recover the jewels and find the thieves.
The gang reportedly arrived at 09:30 (06:30 GMT), shortly after the museum opened to visitors.
The suspects arrived with a vehicle-mounted mechanical lift to gain access to the Galerie d’Apollon (Gallery of Apollo) via a balcony close to the River Seine.
Pictures from the scene showed the ladder leading up to a first-floor window.
Two of the thieves got inside by cutting through the window with power tools.
They then threatened the guards, who evacuated the premises, and cut through the glass of two display cases containing jewels.
A preliminary report has revealed that one in three rooms in the area of the museum raided had no CCTV cameras, according to French media.
French police say the thieves were inside for four minutes and made their escape on two scooters waiting outside at 09:38.
Security measures have been tightened around France’s cultural institutions, officials said.
