The retired seven-time world champion slammed his head against a rock on Sunday while skiing in the French Alps and has had two operations to remove bleeding and pressure on his brain.
Prosecutors have opened a probe into the accident, as is common practice in France in such cases, and are exploring the theory that the German was skiing at great speed when he fell.
Michael Schumacher's plight has prompted an outpouring of sympathy from fans and in a message coinciding with his birthday, his family said they were touched by the reaction.
"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," the family said in a statement posted on Michael Schumacher's website.
"We all know he is a fighter and will not give up" they added.
There have been conflicting statements about the speed Michael Schumacher was going at the time of his accident at the Meribel ski resort, where he has a property.
The impact split the helmet he was wearing in two, according to a source close to the investigation.
The Ferrari F1 team, with whom Michael Schumacher spent many years, announced it would on Friday hold a "silent gathering" in front of the Grenoble hospital where he is being treated to mark the birthday of their ex-driver, who is being kept in an induced coma.
Michael Schumacher's fan club in his childhood town of Kerpen said any celebration of the birthday would be in bad taste.
Jean Todt, former head of the Ferrari team, visited Schumacher's bedside on Thursday. Michael Schumacher's wife Corinna, their two teenage children, and his father and brother were also there.
The hospital and Schumacher's manager had briefed the press daily since the accident. But they did not do so on Thursday, instead promising to communicate only if there was something new to report.
His media representative, Sabine Kehm, said Wednesday that Michael Schumacher was stable though still critical.
Hospital under intense media pressure
The hospital has been faced with intense media pressure due to the worldwide interest in its famous patient. A vacant lot nearby has been turned into an impromptu parking area for numerous television satellite vans.
Kehm earlier in the week said some people had tried to sneak into Michael Schumacher's room, one dressed as a priest.
The three medical professors treating him two neurosurgeons and the head of the anaesthetic and intensive care department have also been thrown into the spotlight. They have appeared at press conferences to explain the latest developments. While they have refused to speculate on how Michael Schumacher's condition may evolve, they say his age and fitness could help with recovery.
Yet questions have emerged over exactly how the accident happened on a small, seemingly innocuous off-piste section of Meribel located between two ski slopes one classed as easy and the other as intermediate.
The prosecutors are looking at whether the limits of the pistes next to the area where accident happened were correctly marked, and whether the safety releases on Michael Schumacher's skis operated properly.
German newspaper Bild reported the skis were rented and one of their safety releases did not open at the moment of the accident.
Prosecutors were not expected to make any statement on the investigation until early next week.
Kehm said this week that the former racer was not skiing fast when he fell.
"He seems to have hit a rock as he took a turn. It was a chain of unfortunate circumstances," she said.
She added that Michael Schumacher was with his 14-year-old son Mick at the time of the accident, as well as a small group of friends.
"He was not going quickly, because it seems he helped a friend who had fallen down," she said.
Michael Schumacher, who made his debut in 1991, dominated Formula One, winning more world titles and races than any other driver.
He first retired aged 37 but was unable to resist the lure of the track. In 2010, he came out of retirement but was unable to recover his previous performance and quit for good in 2012.
As an F1 racer, Michael Schumacher was known for his daring overtaking manoeuvres, his at-times almost reckless abandon in the pursuit of victory and his mastery of tricky conditions presented by rain.