Anthony Jelonch's Six Nations campaign was likely over after the France flanker suffered possible torn ligaments in his knee in their 32-21 win over Scotland on Sunday.
"We don't have good news: the first diagnosis is a rupture of the inner cruciate ligament," Galthie told a news conference.
"You know the protocol for this type of injury. It takes almost six months between the surgery and the rehabilitation. That's also why our joy is moderate this evening."
Jelonch, one of France's toughest defenders, sustained the injury after 25 minutes.
He had already had to go through a concussion protocol following a shoulder charge from Grant Gilchrist, which resulted in the Scotland lock being sent off after seven minutes.