The French Federation (FFR) confirmed the news on Saturday morning, but did not state whether Dupont would play again at the tournament.
The 26-year-old sustained the injury in Thursday's 96-0 record win against Namibia in a head-to-head clash with opposing captain Johan Deysel, whose initial yellow card was upgraded to a red.
"Following his injury sustained during the France-Namibia match, Antoine Dupont underwent surgery at Toulouse's CHU Purpan on 22 September at around 11 p.m.," 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 flyhalf Romain Ntamack at the World Cup due to injury, next face Italy on October 6.