The Welt newspaper reported that fans sung songs and carried banners, but the police had to intervene to stop some of them trying to get into the hospital, where Schumacher has been in a coma since a ski accident on Sunday.
Ferrari, who Schumacher won five world titles with, bussed fans in from Italy to the hospital in the southeastern French city of Grenoble. It also put out a special message on its website, saying "Forza Michael," or "Go Michael" in Italian.
"He is tackling the most important fight of his life and therefore we want to send him very special wishes," Ferrari said, as similar messages poured in from around the world.
German former tennis ace Boris Becker wished Schumacher "Happy Birthday" on Twitter, adding "Fight Schumi" in a German hashtag.
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. He is being kept in an induced coma.
In a message coinciding with his birthday, Schumacher's family said they were touched by the support.
His family is at his side, including his wife Corrina, his two teenage children, his father Rolf and brother Ralph, who is also a racing driver.
"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 Schumacher's website.
"We all know he is a fighter and will not give up" they added.
Fans meanwhile left a poster outside the Grenoble hospital in English, saying "Schumi, All our Thoughts for You and Your Family."
Ferrari tribute creates stir
The Ferrari tribute has created controversy with some accusing the Italian firm - which asked fans to sport red, its colour, and its insignia - of exceeding the limits of good taste.
The Italian carmaker, which has 130 clubs in Europe has provided about 20 coaches across Italy to bus in fans for the ceremony.
But not everyone was pleased, like Roberto Luongo, the president of the Roma-Colesseo Ferrari club, who said he did not want to be associated with any such event linked to "a man who is suffering.
"It's very delicate and if I was among those who are close to Michael, such an initiative would not have pleased me," he said.
Schumacher's fan club in his childhood town of Kerpen said any celebration of the birthday would be in bad taste.
There have been conflicting statements about the speed 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 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 on Wednesday that Schumacher was stable though still critical. Schumacher has had two operations to remove bleeding and pressure on his brain.
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 Schumacher's skis operated properly.
Prosecutors were not expected to make any statement on the investigation until early next week.
Schumacher, who made his Formula One debut in 1991, dominated the sport, 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 could not recover his previous levels of performance and quit for good in 2012.
As an F1 racer, 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.