The 34-year-old victim, who has not been named, died on Saturday evening after being struck by a single bullet while cycling in thick woods near the resort of Les Gets.
The hunter responsible is believed to be a man in his early 20s, and it has been reported that he was treated for shock.
Dozens of gendarmes surrounded the area where the tragedy happened, as others attempted to contact the victim's next of kin.
The mountain biker was reportedly wearing bright and luminous clothing, but the hunter is said not to have seen him.
"It may be that he was mistaken for a fast moving animal".
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One person has already died due to a hunting accident in Gironde, south-west France.
The death is the latest in a series of fatal shootings involving hunters in France in recent months.
The prosecutor also suggested that the gun might have gone off accidentally, but added that he is under investigation for aggravated manslaughter. "He now faces trial and prison".
Last October a woman was killed in her garden after a hunter's stray bullet passed through her garden hedge.
In 2016, there were 18 deaths during hunting accidents in France, and scores of injuries.