The 44-year-old German was in hospital in Grenoble and under the care of Professor Gerard Saillant, a brain and spinal injury expert who is also president of the International Automobile Federation (FIA) Institute.
"He suffered head trauma with coma that needed prompt neurosurgical treatment," Schumacher's agent Sabine Kehm said in a statement late in the evening, which a hospital official read to reporters.
"He remains in a critical condition."
A hospital official declined to give more details but said more information would be given on Monday.
Christophe Gernigon-Lecomte, the director of the Meribel ski resort where Schumacher has a vacation home, said earlier that the former champion was wearing a helmet when he fell and hit his head on a rock at around 11 a.m. local time.
He added that the German had been conscious while being transported first to a local hospital in Moutiers before then being transferred to Grenoble.
"He was conscious but very agitated while being taken to hospital," said the director.
In Germany, Schumacher's accident topped news bulletins, with the bestselling tabloid newspaper Bild reporting on its website: "Schumi fighting for his life".
Bild reporters also said that Ross Brawn, the Briton who worked with Schumacher at Ferrari and Mercedes as technical director and team principal respectively, had arrived in Grenoble.
Schumacher is the most successful Formula One driver of all time with a record 91 race victories in an extraordinary - and frequently controversial - career spanning more than two decades.
He won his first two titles with Benetton in 1994, the year when Brazilian triple champion Ayrton Senna died in a crash at the San Marino Grand Prix, and 1995.
The German then took five in a row with Ferrari between 2000 and 2004 in what now seems a golden age for the Italian team who named a square after him at their Fiorano test track.
Schumacher left the sport last year after a less successful three-year comeback with Mercedes following an earlier retirement from Ferrari at the end of 2006. He lives in Switzerland with his wife and two children.
Image: Michael Schumacher
Photograph: Clive Mason/Getty Images
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