They warned it could be some time before the seven-time champion was “out of danger”.
The German is in a medically-induced coma at University Hospital in Grenoble after suffering head injuries on Sunday in a skiing accident in the French Alps.
Doctors yesterday revealed a scan on Monday night showed “an improved situation” and indicated a window of opportunity for a second operation.
They said the family took the “difficult decision” to give consent for the procedure, and doctors operated on Schumacher for about two hours.
Yesterday, reports emerged that the racing star had been going to help another skier who had fallen on the slopes in Meribel when he fell himself and hit his head on rocks.
Dr Jean-Francois Payen, head of the intensive care unit, said: “We can’t say he is out of danger but we have gained a bit of time, The coming hours are crucial.
“All the family is very much aware that his state is still sensitive and anything can happen.”
Schumacher’s manager Sabine Kehm said the former racing driver’s helmet cracked on impact when he fell.
She said: “It looks like probably that initiating a corner, he hit a stone which he had not seen and was catapulted down on a rock.
“That does not mean that Michael was travelling at high speed. He was not too fast.”
Doctors have said the sportsman would have been killed had he not been wearing the helmet.
Gerard Saillant, a surgeon and a friend of the family who is in Grenoble, said it would be “stupid” to make any predictions about Schumacher’s recovery.
He added: “We cannot tell you any more about the future.”
Schumacher and his 14-year-old son were skiing in the resort, where the family has a chalet, when he fell and hit the right side of his head.
Dr Emmanuel Gay, the hospital’s chief neurosurgeon, said the second brain scan showed bruising “a little bit everywhere” but also an unexpected easing of pressure.
“The brain scan was, I must say, surprising,” he said.
But he and other doctors cautioned that Schumacher’s condition was still grave after surgery to eliminate the largest and most accessible bruise, on the left side of his brain.
Dr Gay added: “We cannot say he is out of danger.”
Schumacher, who is 45 on Friday, retired from F1 last year after garnering an unmatched seven world titles. He is known to be an avid skier, skydiver and horse-rider.
A number of friends and family have visited him in hospital, including former teammates from his time at Ferrari, with whom he won five of his record seven F1 titles from 2000-4.
Former Ferrari teammate Felipe Massa, who recovered from life-threatening head injuries he suffered at the 2009 Hungarian Grand Prix, wrote on Instagram: “I am praying for you my brother! I hope you have a quick recovery! God bless you, Michael.”
A spokesman for German chancellor Angela Merkel said she and her government were, like millions of Germans, “extremely shocked”.
Arsenal manager Arsene Wenger said: “We are all shocked that a man who has taken so many risks in his life and got out of every single risk he took, with a simple accident this can happen to him, which can happen to anyone else who is not as gifted on the sporting front.”
News presenter Piers Morgan tweeted: “Docs say Schumacher showing ‘surprising improvement’. Won’t be a surprise to anyone who saw him race. Come on, Michael.”