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.
But when Schumacher then fell into coma, doctors realised 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.
The next update on Schumacher's condition would be given at 1000 GMT on Monday, a hospital spokesman said.
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.
A towering figure in Formula One
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.
Schumacher's duels in his heyday with Damon Hill and Jacques Villeneuve, fired by an unquenchable competitive spirit, have gone down in Formula One lore.
Schumacher was born in January 1969 near Cologne, Germany, the son of a bricklayer who also ran the local go-kart track, where his mother worked in the canteen.
By 1987, Schumacher was the German and European go-kart champion and was soon racing professionally. In 1991 he burst into Formula One by qualifying seventh in his debut race in Belgium and a year later he was racing for Benetton, where he won his first Formula One grand prix in 1992.
After joining Ferrari in 1996, Schumacher achieved infamy by trying to ram Villeneuve off the road at Jerez in the last race of 1997, and was disqualified from the championship as punishment.
Over the next decade, he went from strength to strength, dominating the podium, before trying to retire the first time aged 37.
But the father of two could not resist the lure of the track and in 2010 he signed a three-year deal with Mercedes.
But slower reflexes and a less competitive car meant Schumacher could not reproduce his former glory and he quit for good in 2012. His helmet had a message for fans: "Life is about passions -- Thank you for sharing mine."