The badly wounded girl died onboard a helicopter that was rushing her to hospital after the 40-year-old man slammed into her at full speed as she was taking part in a lesson organised by the French Ski School (EFS) in Flaine, northwest of Chamonix, on Saturday morning with four other children.
The girl had been on a skiing holiday with her parents who live in Geneva and own a holiday home in nearby Carroz, the local paper Le Dauphine reported.
The man, a volunteer firefighter, tried to give first aid to the girl immediately after the accident, the paper said. He was taken into custody on Monday.
The ski instructor who led the group of children in perfect weather conditions, and who was questioned as a witness, was not found to be at fault in any way, Le Dauphine said.
Prosecutors in the nearby town of Bonneville said excessive speed was the cause of the accident.