The FFR did not say how long Dupont would be unavailable.
"Following his injury sustained during the France-Namibia match, Antoine Dupont underwent surgery at Toulouse's Purpan University on September 22 at around 11pm," the federation said in a statement.
"In a few days' time, he will be able to return to the French team as part of a gradual sporting recovery under medical supervision."
The FFR did not say when Dupont would be able to play again.
France, who are already without fly half Romain Ntamack at the World Cup due to injury, next face Italy on October 6th. It is likely to be a must-win game for Les Bleus unless the Italians can beat New Zealand on September 29th.
France could face top ranked Ireland or defending champions South Africa in the quarter-finals on the weekend of October 14th-15th.
Dupont is expected to miss at least the Italy game, which leaves coach Fabien Galthie to choose between Baptiste Couilloud and Maxime Lucu to replace the 2021 World Player of the Year.
France have won 27 of 31 tests with Dupont in their ranks and lost four of 11 in his absence.
