"Get well soon Michael! Hope to hear some positive news very soon! #strongman," read the tweet sent out by Alonso on Monday.
The message of support, which has been retweeted more than 9,000 times, is one of numerous displays of affection and concern being sent out by Formula One drivers and other sporting figures to the German racing legend.
Get well soon Michael! Hope to hear some positive news very soon! #strongman— Fernando Alonso (@alo_oficial) December 30, 2013
Schumacher, who turns 45 at the end of the week, had been skiing off-piste on Sunday with his 14-year-old son in Grenoble (south east France) when he fell and hit his head on a rock.
Doctors at the hospital where he is being treated have said it was still too early to make a prognosis on the famous patient.
"We can not comment on the future of Michael Schumacher," Jean -François Payen, head of the intensive care unit, told reporters.
"He is in critical condition. He is in intensive care, his condition is very serious," said Payen. "We are working hour by hour," he said, adding that for the moment no further surgery was planned for Schumacher.
Alonso was once regarded as the most likely successor to the German seven-time Formula One champion.
In 2005, the Spaniard became the youngest champion of all times at the age of 24 and in the process ended Schumacher's five year dominance of the Formula One championships.
In a 2010 interview with the BBC, Alonso said: "the most dangerous champion for me is always Michael.
"He is seven-times champion. He has nothing to prove. He is still super class," Alonso said of Schumacher when talking about the problems he was having with his Ferrari.