The 44-year-old German was "suffering a serious brain trauma with coma on his arrival, which required an immediate neurosurgical operation," the hospital in the southeastern French city of Grenoble said in a brief statement.
"He remains in a critical condition," the statement said.
Schumacher had been skiing off-piste with his 14-year-old son in the upmarket Meribel resort, where he reportedly has a property, when he fell and hit his head on a rock.

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He was airlifted to a local hospital, then, an hour later, to the better-equipped Grenoble facility. A surgeon and brain specialist from Paris was rushed in to oversee his treatment.
The director of the Meribel resort, Christophe Gernigon-Lecomte, had said just after the accident that Schumacher had been wearing a helmet and was "conscious but a little agitated", suggesting he had not received life-threatening injuries.
But when Schumacher then fell into coma, doctors realized the damage was worse than initially feared.
Two mountain police officers who gave first aid to Schumacher said he was suffering "severe cranial trauma" when they got to him and a helicopter was brought in to evacuate him within 10 minutes.

A renowned Parisian neurologist, doctor Gerard Saillant, arrived at the Grenoble hospital in a police car to help take charge of the famous patient.
Schumacher's wife Corinna was at his side with his two children, the hospital said.
Police kept guard at the hospital's entrances as journalists and fans, some wearing the colours of the Formula One legend's former stable Ferrari, gathered outside awaiting news of his health.
The hospital statement was signed by the facility's neurosurgeon, the professor in charge of its anaesthesia/revival unit, and the hospital's deputy director. It was issued jointly with the ex-racer's press team in Germany.
Schumacher, who lives with his family in Switzerland, was on a private stay in Meribel, according to his spokeswoman. He celebrates his 45th birthday next Friday.
Police have opened an investigation into the circumstances of the accident, the ski resort said.
Schumacher, who won the last of his world titles in 2004, definitively retired in 2012 in the Brazilian Grand Prix, in which he finished seventh, after an abandoned attempt to quit six years earlier.
Since his debut in 1991, the German towered over the sport, winning more Formula One world titles and races than any other. He had a record 91 wins and is one of only two men to reach 300 grands prix.


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