The 34-year-old Sandstod, who rides for the Danish CSC team of French hero Laurent Jalabert, suffered a collapsed lung and broke eight ribs while descending one of the climbs on Thursday.
No one saw the crash as Sandstod was in between the peloton and stage leader Jalabert. However, it was serious enough to leave doctors worried at the hospital in Tarbes, at the foot of the Pyrenees.
The rider wasn't wearing a helmet, and admitted to his wife Annette: "I thought I was going to die when I crashed."
Annette Sandstod was waiting to watch her husband ride by on the day's final climb and was telephoned from Denmark to be told about the crash.
Sandstod will remain in intensive care for at least 10 days.
The rider, whose contract runs out at the end of the year, has received the support of team manager Bjarne Riis.
"Michael came to the Tour this year knowing that he would be riding for a new contract, knowing he had to prove himself but we can conclude that he has proved himself on the first half of the Tour," said Riis, who won the Tour de France in 1996.
He added: "He's probably been one of the best riders on the team for the first half of the race. If he comes back to cycling then he'll be riding for the CSC team next year."
Sandstod, who switched late in his career from track to road racing in 1996, also broke his hip last year, leaving him on the sidelines for most of last season.