The 26-year-old Katusha rider was fifth in the overall standings at the start of Friday's 19th stage but came down on a fast descent and had to be attended to by medics.
He was taken to the hospital in Brancon by ambulance and will remain there overnight for observation.
Dutchman Steven Kruijswijk, who had started the day as race leader but also crashed into a wall of snow on the same Agnel descent, was taken to the same hospital by ambulance.
Race medics said he suffered injuries to his elbow, knee and ankle and will need to undergo X-rays.