The Real Madrid defender has returned to his club for further recovery after discussions between the French and Real Madrid medical teams.
France will open their UEFA Nations League campaign against Turkey on Friday, but Konate will not be involved after being ruled out of the squad.
The French Football Federation confirmed Konate's departure, saying: "In agreement with the coaching staff, and following a cordial exchange between the medical staff of the French national team and Real Madrid, the player is once again available to his club as of today."
Manchester United defender Leny Yoro has been called up to replace Konate in the France squad.
The injury is not expected to keep Konate out for a significant period, giving him time to recover during the international break.
Real Madrid will hope to have the centre-back available when they return to La Liga action against Villarreal at the Bernabeu on 10 October.