The Formula One driver turns 45 today in his hospital bed in Grenoble after suffering critical head injuries in the French Alps on Sunday.
The Ferrari team which he spent many years racing for announced it would hold a "silent gathering" in front of the hospital to mark his birthday.
Jean Todt, former head of the team, visited his bedside on Thursday along with Schumacher's wife Corinna, their children Gina-Maria, 16, and 14-year-old Mick, his father and brother.
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Schumacher has had two operations to remove bleeding and swelling on his brain and is in an induced medical coma.
A statement from his family on his website said: "Following Michael's skiing accident, we would like to thank the people from all around the world who have expressed their sympathy and sent their best wishes for his recovery.
"They are giving us great support.
"We all know he is a fighter and will not give up. Thank you."
The German was injured while skiing off piste in Meribel, France
A source close to the investigation into his crash said his helmet had been smashed "in two" by the impact after he hit his head on a rock on an off-piste section at the popular Meribel ski resort.
Prosecutors have opened a probe into the accident, which is common practice in France in such cases, and are exploring the theory that the German was skiing at great speed when he fell.
The accident has led to an outpouring of sympathy from racing drivers and fans alike.
Brazilian racer Felipe Massa, German Chancellor Angela Merkel, and Arsenal footballers are among the many public figures who have sent messages of support.
But Schumacher's manager has said there have been "constant attempts" to get access to him as he lies in an induced coma.
Sabine Kehm has confirmed that security at the hospital had stopped a journalist posing as a priest from getting into his room.
The German driver is the most successful in Formula One history, racking up a record 91 race wins and seven world titles.
