Schumacher, who turned 45 while in hospital in Grenoble, lost his footing while skiing off-piste in December and landed head-first on a rock.
He has been in a medically-induced coma for over four weeks while fighting for his life but doctors have begun to reduce his sedation.
His manager Sabine Kehm said in a statement: "Michael’s sedation is being reduced in order to allow the start of the waking up process which may take a long time."
Kehm explained the family had decided to brief the media on Schumacher's latest condition following a leak to French paper L'Equipe, which first revealed on Wednesday that doctors had started waking the star.
Her statement continued: "The family of Michael Schumacher is again requesting to respect its privacy and the medical secret, and to not disturb the doctors treating Michael in their work.
"At the same time, the family wishes to express sincere appreciation for the worldwide sympathy.
"For the protection of the family, it was originally agreed by the interested parties to communicate this information only once this process was consolidated. Please note that no further updates will be given."
Reports had suggested last week that Schumacher’s chances of a full recovery were to diminish the longer he was held in the induced coma.
Jean-Marc Orgogozo, professor of neurology at the University of Bordeaux, was quoted by the Daily Mirror as saying: “Every day, every week in a coma the chances decline that the situation is improving.”
French police have said Schumacher was not skiing recklessly when he crashed and hit his head on a rock.