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 scrumhalf, 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 22 September," 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.
Touché mais pas coulé. Show must go on ⚔️. Hâte de retrouver le groupe ⏳
— 𝗔𝗻𝘁𝗼𝗶𝗻𝗲 𝗗𝗨𝗣𝗢𝗡𝗧 (@Dupont9A) September 23, 2023
Merci pour vos messages pic.twitter.com/KCJYJp3Fit
He is in a race against time to be able to play in France's final pool game against Italy on 6 October with a potential quarterfinal against reigning champions South Africa or Ireland, the world's No 1-ranked team, looming on the weekend of October 14-15.
"We are not going to make plans too soon," said France's assistant coach Laurent Labit.
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 semifinal."
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".
'LEVEL OF DANGER'
A long absence for Dupont would be a severe blow to France's hopes of winning the World Cup for the first time.
Former Les Bleus back-rower Olivier Magne warned about bringing Dupont back too soon.
"There's three weeks before the quarterfinal but this type of injury is not benign," Magne told AFP.
"There's a level of danger that is significant with an early return, so you have to be vigilant.
"There's a problem with the message it sends out to the general public by allowing a player back after such a serious injury," he added.
Maxime Lucu and Baptiste Couilloud are the other two scrumhalves in the France World Cup squad and Edwards said they were "brilliant scrumhalves and brilliant leaders who will step up".
Flyhalf Romain Ntamack did not even make the squad because of injury with first-choice hooker Julien Marchand and No 8 suffering from fitness issues during the tournament.
With Dupont out, Magne backed ex-skipper Charles Ollivon or the half-back's former room-mate Anthony Jelonch to lead the side.
"That's not a problem. The captaincy is not a subject that poses a problem for France," Magne said.
"There are players that are leaders in the team.
"These players lead the game and there will be a captain named either Charles Ollivon or Anthony Jelonch for the next game," he added.
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.