The 45-year-old German will continue his rehabilitation at an undisclosed location, they said in a statement.

Schumacher was placed in a medically induced coma after suffering a severe head injury in a skiing accident in the French Alps on 29 December.

His family thanked people who had sent messages of support, saying: “We are sure it helped him.”

They also praised the “excellent job” of medical staff at the hospital in Grenoble, in south-east France.

Doctors had kept the seven-time champion in a coma to help reduce swelling in his brain.

Michael Schumacher was being treated at Grenoble’s University Hospital Centre in the French Alps

“Michael has left the CHU Grenoble to continue his long phase of rehabilitation. He is not in a coma anymore,” Schumacher’s manager, Sabine Kehm, said in a statement on behalf of his family on Monday.

“For the future we ask for understanding that his further rehabilitation will take place away from the public eye,” she said, without specifying where Schumacher had been taken to.

Relatives have previously warned that “it was clear from the start that this will be a long and hard fight for Michael”.

Medically induced coma

• Can be induced by powerful anaesthetics and is broadly similar to the sedation and artificial ventilation used during surgery
• Used to shut down many brain functions, lowering blood flow and pressure
• Taking a patient out of an induced coma is a delicate process, especially after a prolonged period of sedation

Meanwhile, the German football team sent well wishes to the F1 legend from the World Cup in Brazil at the weekend.

Lukas Podolski, the Arsenal striker, told a news conference: “I’d like to greet a good friend, who unfortunately is unable to be here. He is Michael Schumacher.

“He is just as crazy about football as all of us. We wish his family a lot of strength. If we win the title, that would be something that would make him happy.”

Michael Schumacher

• Born: 3 January 1969
• First GP win: Belgium 1992
• Last GP win: China 2006
• Races started: 303
• Wins: 91 (155 podium finishes)
• Championships: 7 (1994, 1995, 2000, 2001, 2002, 2003, 2004

Investigators probing the accident said Schumacher had been going at the speed of “a very good skier” at the time of his crash in the resort of Meribel.

He had been skiing off-piste when he fell and hit a rock, investigators said.

Schumacher retired from racing in 2012 after a 19-year career.

He won two titles with Benetton, in 1994 and 1995, before switching to Ferrari in 1996 and going on to win five straight titles from 2000.