AFP have reported he "was suffering a serious brain trauma with coma on his arrival, which required an immediate neurosurgical operation".
Schumacher's management have confirmed his condition, reports the BBC.
The German suffered head injuries in the incident in Meribel, Sky News reported.
Schumacher had just got off a chair lift with his son when he fell.
He was said to have been wearing a helmet.
The driver's agent said he was unable to give a "running commentary" on his condition, after he was airlifted to a local hospital and then moved to a hospital in nearby Grenoble.
The duty manager at the hospital told Sky News earlier Schumacher was undergoing a scan.
Suggested For You
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more