"I am absolutely not ready. Not ready to run, not ready to jump. I'm not fit enough to play in the Olympic Games," Noah told French sports daily L'Equipe.
Noah, who averaged 10.2 points and 9.8 rebounds per game this season, picked up the ankle injury in a play-off game against the Philadelphia Sixers in May.
France are also sweating on Tony Parker's condition as the San Antonio Spurs point guard is doubtful with an eye injury.