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."
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.
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.
