The seven-times Formula One champion has been transferred from the unit in Grenoble, France, to a hospital in Switzerland.
The motor racing star was hurt in the incident in the French Alps in December, and was subsequently put into an artificially-induced coma a few days later.
But his management company said: "Michael has left the CHU Grenoble to continue his long phase of rehabilitation. He is not in a coma any more."
Schumacher's family expressed their gratitude to all those who have played a part in the process over the past five and a half months.
The statement added: "His family would like to explicitly thank all his treating doctors, nurses and therapists in Grenoble, as well as the first aiders at the place of the accident, who did an excellent job in those first months.
"The family also wishes to thank all the people who have sent Michael all the many good wishes. We are sure it helped him.
"For the future we ask his further rehabilitation will take place away from the public eye."
University Hospital of Lausanne (CHUV) in Switzerland confirmed that Schumacher had been transferred there.
Darcy Christen, a spokesman for the hospital, said: "I can confirm that he has been admitted this morning."
He said the hospital would not be disclosing any details about the star's condition or which part of the hospital he is being treated in.
"I can't say anything about his medical status. We have decided to ensure for him and his family, privacy and medical confidentiality," he added.