The 44-year-old German suffered serious brain trauma, was in a coma on arrival and underwent a brain operation Bbc is reporting.
He was skiing off-piste with his son in the French Alps on Sunday when the accident occurred.
Schumacher was wearing a helmet when he fell and hit his head against a rock, his manager Sabine Kehm said.
Early reports had said his condition was not life-threatening and he reportedly walked away from the accident
complaining only of feeling a bit shaken.
The accident took place in the French ski resort of Meribel on Sunday morning.
The resort’s director, Christophe Gernignon-Lecomte, said Schumacher was attended to by two ski patrollers who requested helicopter evacuation to the nearby valley town of Moutiers.
He was subsequently moved to the bigger facility at Grenoble, in south-east France. His wife Corinna and two children are with him.
“Mr Schumacher was admitted to the University Hospital of Grenoble at 12:40 [11:40 GMT], following a skiing accident
which occurred in Meribel in the late morning,” the Grenoble hospital said in a statement.
“He suffered a severe head injury with coma on arrival, which required immediate neurosurgical intervention. He remains in a critical situation.”
The hospital statement was signed by the facility’s neurosurgeon, the professor in charge of its anaesthesia/
revival unit, and the hospital’s deputy director, reports said.
A hospital official declined to give more details and said more information would be given out on Monday, said
Reuters news agency.
Experts say it is likely that his brain began to swell and the urgent surgery was required to relieve the pressure, says the BBC’s Hugh Schofield in Paris.