France captain Antoine Dupont has undergone surgery on a fractured cheekbone and will return to the squad "in a few days", the French Rugby Federation (FFR) said on Saturday.
It is not clear, however, when he will be able to return to the pitch in the World Cup.
Dupont suffered the injury in a clash of heads with Namibia captain Johan Deysel in France's 96-0 pool victory on Thursday.
The 26-year-old scrum-half, who was world player of the year in 2021, had surgery in Toulouse on Friday.
"Following his injury sustained during the France v Namibia match, Antoine Dupont underwent surgery at the Purpan University in Toulouse on September 22," the FFR said.
"He will be able to return to the French team in a few days as part of a gradual sporting recovery under medical supervision," the FFR added.
"Hit but not sunk. Show must go on. I can't wait to rejoin the squad," Dupont said on social media.
He is in a race against time to be able to play in France's final pool game against Italy on October 6 with a potential quarter-final against reigning champions South Africa or Ireland, the world's number one-ranked team, looming on the weekend of October 14-15.
France's assistant coach Laurent Labit said: "We are not going to make plans too soon."
France's defence coach Shaun Edwards said in his column for the Daily Mail on Friday: "It's a very painful injury but a broken cheekbone is easier to manage than a broken jaw.
"If we make it to the latter stages of the World Cup then I'd be very surprised if he isn't available for the quarter or semi-final."
Doctor Bernard Dusfour, former president of the medical commission of the National Rugby League (LNR), told AFP on Friday that after undergoing surgery, the minimum period of unavailability for an elite athlete was "four weeks".
A long absence for Dupont would be a severe blow to France's hopes of winning the World Cup for the first time.
Maxime Lucu and Baptiste Couilloud are the other two scrum-halves in the France World Cup squad and Edwards said they were "brilliant scrum-halves and brilliant leaders who will step up".
Fly-half Romain Ntamack did not even make the squad because of injury.
Deysel, the Namibian who caused Dupont's injury and was red-carded, has apologised.
"I would like to extend my best wishes to Antoine Dupont. Clearly, I meant no harm. Everything happened very quickly and I couldn't get my head out of the way quick enough, resulting in a head clash," he said.
The importance of Dupont is underlined by the fact that he is yet to lose in a France team he has skippered on home soil in 14 Tests.
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