"At the moment, he is tackling the most important fight of his life and therefore we want to send him very special wishes," Scuderia Ferrari, the racing team division of the Italian car maker, said in a Facebook post.
Schumacher, the former world champion racing driver, suffered severe injuries in a skiing accident on Sunday in the French Alps.
He has undergone two operations and is in stable but critical condition at the hospital in Grenoble, France, doctors said.
Scuderia Ferrari invited fans to wear red and attend the silent vigil to mark Schumacher's 45th birthday.
Schumacher's family also posted a message on his official website.
"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," his family said.
Schumacher was the most successful driver in Formula 1 history and won 72 Grand Prix between 1996 and 2006.