Martin Brundle, a former teammate of Schumacher, wrote on Twitter: "Come on Michael, give us one of those race stints at pure qualifying pace to win through, like you used to. You can do it."
The motor-racing legend had been wearing a helmet while skiing off-piste in the upmarket Meribel resort - where he reportedly has a luxury chalet - when he fell and hit his head, said mountain police, who gave him first aid.
He was airlifted to a local hospital, then on to Grenoble, where a specialist neurosurgeon from Paris was rushed to oversee his treatment.
Witnesses said Schumacher was conscious but in an "agitated state" as he was treated by medics on the slopes.
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 1 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.
The two mountain police officers who gave first aid said Schumacher was suffering "severe cranial trauma" when they got to him and a helicopter was brought in to evacuate him within 10 minutes.
A renowned Paris neurosurgeon, Dr Gerard Saillant, was brought to the Grenoble hospital in a police car to take charge of the famous patient, who is to have his 45th birthday on Friday.
A spokesman for the Grenoble hospital where Schumacher was taken said he was "suffering a serious brain trauma with coma on his arrival, which required an immediate neurosurgical operation".
"He remains in a critical condition."
Former French F1 driver Olivier Panis visited the hospital in Grenoble but was not able to see Schumacher.
"Yes, I am worried," he said.
"I know that his family has arrived. As I am here in Grenoble, I want to come to him and say hello, for old times' sake. He is a great champion and someone very loved in Formula 1."
The director of the Meribel resort, Christophe Gernigon-Lecomte, had said 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 his condition deteriorated with doctors realising the damage was worse than initially feared.
French authorities are investigating the circumstances.
Jamie Fox, head of communications for the British ski team who has skied with Schumacher, said: "He absolutely adores skiing but he is incredibly competitive at anything he does."
Hero of the track
* Michael Schumacher was born in January 1969 near Cologne, Germany. His father was a bricklayer who also ran the local go-kart track, where his mother worked in the canteen.
* By 1987, Schumacher was the European go-kart champion and was racing professionally. In 1991 he burst into Formula 1 and won his first grand prix in 1992.
* Over the next decade, he dominated the podium.
* Schumacher's duels in his heyday, with Damon Hill and Jacques Villeneuve - fired by an unquenchable competitive spirit - have gone down in Formula 1 lore.
- AP
