The player suffered the injury during training yesterday and was later taken to hospital for an MRI scan which confirmed the damage down, according to the FFA.
The player was set to start both matches for France against Armenia and Denmark which are being played tonight and next Wednesday respectively.
After the injury was confirmed, the France manager Didier Deschamps decided to offer the player back to the Italian club "immediately", as it was clear Pogba was not going to see any action over the weekend.