The 44-year-old is said to be in a critical condition as he suffered from a serious brain trauma with coma on his arrival to the hospital.
Sky’s F1 commentator and former driver Martin Brundle, who was Schumacher's team-mate at Benetton, tweeted: "Let's hope Michael Schumacher's ski shunt is not too bad and that he's totally fixable.
British driver Jenson Button tweeted: "My thoughts are with Michael Schumacher at this tough time. Michael more than anyone has the strength to pull through this."
Felipe Massa, the Brazilian driver whose injury brought Schumacher back to F1 in 2009, posted a picture of the pair embracing on Instagram, with the Portuguese message: "I'm praying for God to protect you, brother!
Former F1 driver Giancarlo Fisichella also tweeted: "I know you Michael, you are the man, you are the best you are. This is the most difficult race but I am sure you we will again!
Schumacher, who won the last of his world titles in 2004 and definitively retired in 2012 in the Brazilian Grand Prix, in which he finished seventh, is to have his 45th birthday next Friday.