The FFF says Monday that "in these exceptional circumstances, the coach (Didier Deschamps) has accepted the request of the player." Martial is due to return to the France squad on Tuesday.
The 19-year-old Martial has played at all youth levels for France and has been called up by Deschamps for the first time for upcoming friendlies against Serbia and Portugal.
He scored nine goals in 35 league matches last season and recently extended his contract with Monaco until 2019.
United has scored just three goals in four Premier League games this season.
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