France captain Antoine Dupont sustained a facial fracture in the record victory over Namibia but has not yet been ruled out of the World Cup, the French federation announced Friday.
The highly influential scrum-half left the field visibly in pain in the 46th minute of Thursday's 96-0 rout following a clash of heads with Namibia captain Johan Deysel.
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Dupont, who is yet to lose in a France team he has skippered on home soil in 14 Tests, was immediately taken to hospital in Marseille for scans.
"Specialised surgical advice was requested to assess how long he will be unavailable for," the federation added.
Host nation France, who scored a French record 14 tries in their third consecutive win in the tournament, are scheduled to play their final Pool A match against Italy in Lyon on October 6.
Media reports said 26-year-old Dupont would be sidelined for a month, meaning he would miss not only the game against Italy, but also the World Cup quarter-finals on the weekend of October 14-15.
Deysel was initially handed a yellow card, later rightly upgraded to red, although Namibia coach Allister Coetzee described the clash of heads with Dupont as an "unfortunate accident".
Prop Cyril Baille said Dupont's injury had completely overshadowed a dominant French performance over Namibia, who are yet to win a World Cup match after 25 matches in seven tournament appearances.
"We know how important he is in the squad, what he brings," said Baille. "When you look at the images, it's a pretty violent impact. It tarnished the evening somewhat, there's a lot of stress.
"Of course we're happy with the scoreline, but it wasn't a party in the changing room after that."
Flanker Francois Cros, who like Baille is a teammate of Dupont at Toulouse, said that if his injury turned out to be serious, "it would obviously have an impact on him and on us".
"Watching the replay, we knew the decision the referee would make. But we had no idea about Toto's (Antoine Dupont's) condition. We didn't know if he was going off as a precaution or if he was really hurt until the end of the match."
Cros added: "We still have some experienced nines who can take over."
Lyon's Baptiste Couilloud came on for Dupont and was full of running as he scored a try of his own, almost with his first touch, as he ensured the French team re-discovered their rhythm after a raft of replacements.
The third scrum-half in the 33-man squad is Bordeaux-Begles' Maxime Lucu, who won the man-of-the-match award in France's second pool match against Uruguay as he marshalled the team sufficiently in the second-half to victory over the South Americans.
Galthie faced questions after the match about whether Dupont should have been taken off at half-time of a game France were clearly going to win.
"What do you want me to say? You can't take 14 players off at half-time. Our plan was to bring off one, three and five at half-time, then the rest at the 55th minute," he said.
"The aim was to give everyone some game-time and not sit back for a month. The players wanted and needed to play.
"Our next match is in 15 days. We'll take stock of everyone's condition and quickly put together a team," Galthie said.
"The training cycle is already scheduled. We'll stay here, have three days off and then start another week of training."
There was sympathy for Dupont from other countries, with England defence coach Kevin Sinfield expressing hope he would soon be back in action.
"I'm disappointed for the competition at this moment in time but we have no doubt he'll be back," Sinfield said.
"World-class players like that get themselves right very quickly and I'm sure he's doing everything he can."
France, who have never won the World Cup, began with a morale-boosting 27-13 tournament-opening win over New Zealand before a largely second-string side laboured past Uruguay 27-12.
