Schumacher has been in a medically induced coma since a skiing accident at the Meribel resort in France on Sunday.
Schumacher remains in a critical but stable condition in Grenoble hospital.
Ferrari clubs from Italy and France gathered outside of the hospital on Friday and unfurled a giant Ferrari flag to show their support for the injured German.
Over 200 fans joined a silent vigil, which left Schumacher's family 'overwhelmed'.
'We are overwhelmed! The incredible sympathies shown today by the Ferrari Fans outside the hospital has utterly overwhelmed us and moved us all to tears', read a message from Schumacher's family on his official website.
'We are deeply grateful for it and also for all the heartwarming and heartfelt wishes for Michael to get well soon, which have reached us from all over the world.'
Schumacher's close family, including wife Corinna, brother Ralf and father Rolf, have been at his bedside throughout the week.