Two of those arrested are under formal investigation for suspected theft.
The other four are suspected of concealment of theft, the source said.
The thieves are believed to have used portable grinders to remove the emergency exit door on which the mural was painted before transporting it in a van, Italian media reported when the work was discovered.
Bataclan, one of the most famous rock sites in Paris, was attacked by activists during a concert in November 2015, in the context of coordinated attacks around the city that killed 130 people
Australian Associated Press