The train was travelling from the coastal city of Nice to the town of Digne-les-Bains and came off the tracks after hitting a rock on the rails, they said.
Emergency services rushed to the scene and a red alert, meaning "several victims", was issued. Firefighters from around the region were drafted in to help.
A total of 110 firefighters and 32 vehicles were deployed, as well as two helicopters.
One of the injured is in critical condition and eight others, including the driver, sustained lighter injuries, the fire service said.
Authorities encountered difficulties in reaching the accident due to heavy snow and an isolated location.
In July, seven people were killed when a commuter train derailed near Paris.