The FFR, which did not give details on Ntamack's injury, said the 21-year-old was being replaced in the 31-man squad by Toulon's Louis Carbonel.
Ntamack has started France's six tests under new coach Fabien Galthie alongside scrumhalf Antoine Dupont and the pair are developing into one of the world's most formidable halfback partnerships.
France finished second in the Six Nations, behind England on points difference.
Their Autumn Nations Cup opener against Fiji on Sunday was called off because of COVID-19 cases within the Fijian squad.
(Reporting by Julien Pretot; Editing by Ed Osmond)