Coulthard, now a BBC motor racing commentator and who had many on-track battles against the seven times world champion, said his thoughts were with Schumacher, who is in an induced coma in intensive care.
The 44-year-old remains in a critical condition after undergoing emergency surgery for a severe head injury he sustained while skiing off-piste with his son in the resort of Meribel.
Doctors performed the surgery remove a blood clot that was pressing on his brain. They are now keeping him in a state of hypothermia, in an attempt to reduce pressure caused by the swelling of his brain.
They said Schumacher survived Sunday's accident in Grenoble, France, only because he was wearing his ski helmet.
Coulthard, who finished runner-up in the Formula One world championship to Schumacher in 2001, said he was confident the star's athleticism and determination would help him.
The Scot, who is on a skiing break in the Alps said: "This is a freak accident, it's not the first one we have seen this winter in the Alps.
"All the cards are stacked in his favour. As I know Michael from the racetrack there is no question in my mind he has the physical ability to take on this challenge, which will undoubtedly help him to come through what is the greatest challenge of his life.
"There is a high risk in skiing generally, we all know that, but doing it off-piste is a bit like driving a car quickly on the race track."
He added: "You don't know if there is a tree stump below that powder of snow, you don't know whether there's a rock. And that is probably part of the enjoyment of doing that type of thing."
His comments came as messages of support for Schumacher poured in from across the motor racing community. Quadruple Formula One world champion Sebastian Vettel said: "I am shocked and I hope he will get better as quickly as possible. I now wish his family a lot of strength."
Dario Franchitti, the Scottish-born former IndyCar champion, who recently retired from the sport after being injured in a race crash, said: "My thoughts are with Michael and his family. If anyone can pull through this it's him."
Jenson Button, the 2009 F1 champion, said: "My thoughts are with Michael Schumacher at this tough time. Michael, more than anyone, has the strength to pull through this."
Schumacher's friend and his former Ferrari team-mate Felipe Massa said: "I'm praying for God to protect you, brother!"
Schumacher's family thanked everyone who gave their support. They said: "We would like to thank the people from all around the world who have expressed their sympathy and sent their best wishes for his recovery. They are giving us great support."
Jean-Francois Payen, the chief anaesthetist at the Grenoble University Hospital Centre, where Schumacher is being treated, said: "It is too early to make a judgement about the future of Michael Schumacher. His situation is critical. Given the violence of the shock, his helmet protected him in part. Someone who had not been wearing a helmet would not have got here."