The seven-time Formula One world champion is in a medically-induced coma in hospital in France after being injured in a fall while skiing in Meribel on Sunday.
Schumacher was initially airlifted to a local medical facility before being transferred to the University Hospital of Grenoble, with early reports suggesting that his injuries were "not very serious".
However, the 44-year-old German's condition deteriorated on Sunday night, with the hospital revealing in a statement that he had suffered a head trauma that required "immediate neurosurgical treatment".
There had been speculation of a second operation overnight, but in an update to the gathered media on Monday the doctors treating him confirmed that had not been the case.
They also revealed that his use of a helmet had more than likely prevented him from being killed, although his future prognosis remains highly uncertain.
"He is in a critical condition," professor Jean-Francois Payen told a press conference. "His condition is considered to be extremely serious and he is in intensive care.
"Our neurological team are working all together to treat him. We are currently talking about treatment, working hour by hour.
"The helmet did protect him to a certain extent, of course. Someone without a helmet wouldn't have got to here.
"But the situation is critical and his condition is serious. It is far too early to be able to say as far as his prognosis is concerned."