Two of the donkeys were killed instantly; the other two were badly injured and had to be put down, the Arpi'âne company said in a Facebook post on Sunday, blaming an unnamed Swiss hunter as the culprit.
The man was hunting in Arith, in the Bauges regional park, near the pasture where the donkeys were grazing. He shot at them most probably as they came out of the wood, said the post.
“In the Bauges, in the 21st century, people shoot at animals who come out of the woods without bothering to check what they're shooting at,” said the post.
The company also accused the man of failing to call a vet and fleeing when he realized he had shot at domestic animals.
According to Le Matin, the hunter and his brother had paid for a hunting permit in the area.
It was the local hunting association that came to apologize to the donkeys' owner, though it gave no explanation for the Swiss man's mistake.
Speaking to local press, the director of the Savoie hunting federation condemned the incident, saying it was "incomprehensible" and "bad for the image of hunting in Savoie".
The 8,000 hunters in the region "are not like that Swiss hunter," he said.
The Arpi'âne company, which hires out its donkeys for walks in the Bauges forest, said for the moment it would no longer do so, but would take care of its sole remaining donkey.
Accidents during hunting season are not uncommon.
Last year in the canton of Graubünden a hunter admitted to killing a rare golden jackal after mistaking it for a fox.
Several hunters also lost their lives last season after falling in the mountains.
This year, a boy was killed by his grandfather on the opening day of hunting season in the Vendée, France.
The 13-year-old was shot in the head as he went to pick up a game bird that had been shot.
In 2012 a 60-year-old was shot by hunters in the Swiss canton of Fribourg after they mistook him for a wild boar. He was in fact picking cannabis leaves.