Holding midfielder Diarra left the squad on Saturday after missing training for three days because of persistent stomach pains.
The 25-year-old, who has won 27 caps and was regarded as a likely starter, suffers from a genetic blood disorder affecting red blood cells and causing chronic fatigue, his Real Madrid club said in a statement.
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"It's hard to swallow because we know the importance of Lass (Lassana) on and off the pitch," defender Sebastien Squillaci told reporters on another gorgeous day in this scenic French Alps resort surrounded by rugged snow-capped peaks.
"Blows like this often bring the players more closely together," Squillaci added. "We will think about him, he will be in our heads."
Diarra, who started feeling unwell on a hike up a glacier overlooking the ski village where France are in a week-long training camp, will have to rest for an indeterminate period, a France team spokesman said.
"I saw him wake up and get dressed at six in the morning (on Thursday) and tell us he was not feeling well and was going to hospital," defender Gael Clichy told reporters.
"WILL RECOVER"
Later that day, Diarra, whose illness might have been aggravated by altitude, could not train and was seen talking to Raymond Domenech for 45 minutes.
"He's suffering but he will recover, that's for sure, and this will have no effect on the rest of his career," the France coach told French television channel TF1.
The mood at the France camp was sad but combative.
"It's always tough to see a mate go," Clichy said. "We're thinking about him and we hope this will make us stronger. It could have happened to any of us and it's even tougher because he's a good guy. We promised ourselves we would fight for him."
Domenech, who had taken a provisional 24-man squad to Tignes, has not yet decided whether Diarra will be replaced.
"It's difficult to tell, when you lose a player, if you are going to take another one," the coach said. "We have a few days to make a decision, we will see."
Domenech, who has until June 1 to name his final 23-man squad, had picked 24 players because of a question mark over the fitness of William Gallas.
Centre-back Gallas, who suffered a recurrence of a calf muscle injury in late March and has not played since, completed Sunday's two-hour session, raising hopes he would be fit for the World Cup which starts on June 11.
France face hosts South Africa, Mexico and Uruguay in Group A.#
