Pogba left training early on Wednesday and underwent an MRI scan on Thursday which confirmed a sprain to his right ankle.
The 22-year-old has been given permission to return to his club by France coach Didier Deschamps.
A statement released by the French Football Federation read: "Paul Pogba who had to leave training prematurely on Wednesday night, spent Thursday morning an MRI which confirmed a stage 1 sprain of the right ankle.
"Given the inability of the player to play two matches in the France team programme this weekend (France-Armenia in Nice [on] Thursday and Sunday [against] Denmark [in] Copenhagen), Didier Deschamps decided to make the player available for his club this Thursday afternoon."