Schumacher has been placed in a medically induced coma to relieve pressure on his brain, which suffered bruising and bleeding when the retired seven-time world champion fell and struck a rock on Sunday while skiing during a family vacation.
"We cannot predict the future for Michael Schumacher," Jean-Francois Payen, the doctor in charge of Grenoble University Hospital's intensive care unit, said at a news conference.
"He is in a critical state in terms of cerebral resuscitation," said Payen, the chief anaesthesiologist treating the 44-year-old German driver.
"We are working hour by hour."
Schumacher's wife, Corinna, daughter Gina Maria and son Mick were at his bedside.
Schumacher earned universal admiration for his uncommon driving talent, which led to a record 91 race wins. His single-minded dedication to victory sometimes meant he was denied the same affection during his career that he received Monday.
Schumacher and his 14-year-old son were skiing Sunday morning in the French Alpine resort of Meribel, where the family has a chalet. He fell and hit the right side of his head on a rock.
By wearing a helmet, Schumacher had given himself a chance of survival, Payen said, though the protection was not enough to prevent serious injury.
Gerard Saillant, a trauma surgeon who operated on Schumacher when he broke his leg in a 1999 race crash, was at the hospital as a visitor.
He told reporters that Schumacher's age and fitness should work in his favour.
Schumacher, who turns 45 on Friday, retired from the track for the second time only last year, after a three-season comeback.
Still, the hospital's neurology team, which is recognised as among the best in France, was cautious about Schumacher's prospects.
Doctors lowered his body temperature to between 34 and 35 degrees Celsius (93.2 to 95 degrees Fahrenheit) as part of the coma, which essentially rests the brain, slowing its metabolism to help reduce inflammation after an injury.
The hospital, in a city that is the gateway to the French Alps, sees a large number of skiing accidents every year.
Schumacher has been seriously hurt before. In addition to the broken leg in a crash at the 1999 British Grand Prix, he also suffered neck and spine injuries after a motorcycle accident in 2009 in Spain.
An expert skier, Schumacher fell in a section of trails that slice down through a vast and, in parts, very steep snowfield.
Although challenging, the snowfield is not extreme skiing. The runs are broad and neatly tended, and the ungroomed area in between - where the resort said Schumacher was found - is free of trees.
Meribel resort officials said Schumacher was conscious when first respondents arrived, although agitated and in shock.
After the fall, Payen said Monday, Schumacher was not in a "normal state of consciousness." He did not respond to questions, and his limbs appeared to move involuntarily, the doctor said.
He was airlifted to a local hospital and then later brought to Grenoble. Doctors said that stopover was typical and did not affect his condition.
The French prosecutor in Albertville has opened an investigation into the accident, according to the Mountain Gendarmerie in Bourg-Saint-Maurice.
The goal is to determine the circumstances and cause of the accident.
GERMAN FANS, SPORTS STARS SHOCKED BY SCHUMACHER ACCIDENT
Chancellor Angela Merkel joined sports legends and millions of Germans on Monday in expressing shock at Formula One great Michael Schumacher's skiing accident, as his family thanked well-wishers for their support.
In Schumacher's home town of Kerpen, North Rhine-Westphalia, locals were also wishing for a quick recovery for the daredevil racing driver who first honed his skills on his father's local go-kart track as a youth.
"He was always searching for risk and speed," town mayor Marlies Sieburg told AFP, adding that "of course he is a fighter, maybe that will help him".
"The fan club and many residents are concerned not only for the Formula One champion but also for the human being, the man."
Merkel declared herself "extremely shocked along with millions of Germans" by the news, according to her spokesman Steffen Seibert.
"We hope, along with Michael Schumacher and his family, that his injuries will heal and he will recover. We wish his wife, his children and the rest of his family strength and mutual support."
Schumacher's wife Corinna and the family expressed their gratitude for the encouragement.
"We would like to thank the medical team who, we know, do everything possible to help Michael," she said in a statement.
"We like to also thank the people from around the world who have expressed their sympathy and sent their best wishes for his recovery."
Formula One quadruple world champion Sebastian Vettel, 26, who has said Schumacher was his childhood idol, said: "I am shocked and I hope that he'll be feeling better as soon as possible.
"I wish his family much strength now."
Other well-known German sporting stars took to social media wishing the racing legend known as "Schumi" a quick recovery.
Tennis legend Boris Becker wrote on Twitter, "Let us all pray for (Schumacher) for a full and speedy recovery !!!", while basketball star Dirk Nowitzki wrote, "My thoughts are with Schumi".
The 22-time Grand Slam winner Steffi Graf wrote on Facebook that "our worries and thoughts are with Michael 'Schumi' and those who are close to him. We wish him a speedy recovery and know that his strength will help him through this difficult situation".
Under the Twitter hashtag #KaempfenSchumi (Fight, Schumi!) many others sent their wishes, including: "Schumi, you must win this race too! It's your most important yet."
Michael Viehmann, president of a Schumacher fan club in Kerpen, said: "We're very upset. We know him really well. He's a fighter, we're crossing fingers that he will win this battle."
The co-chairman of the fan club, Reiner Ferling, said the club had received thousands of emails and hundreds of new membership applications since Sunday.
