The cub, identified as M25, was tracked in the Lower Engadine, where early Thursday it attacked sheep among a herd of 300 animals at Vinadi, media reports said.
“It was a disaster,” Georg Jannett, president of the local association of sheep breeders told the Südostschweiz newspaper.
“If the bear does not vanish we will have to remove the sheep from Vinadi.”
Nine sheep were ripped apart by the bear and two of them were almost completely eaten, the newspaper said.
An injured ewe had to be euthanized, according to the report.
Because the sheep are spread over a vast mountainous area it is difficult to constantly monitor what is happening to them, Jannett said.
Pressure is mounting on officials to kill the bear but environmental group WWF has already launched a petition to protect the animal.
The organization said it does not want M25 to meet the same fate as other bears such as M13 and JJ3 that were destroyed by wildlife officials for security reasons.
WWF said it wants Graubünden’s cantonal government to show leadership on the issue by promoting measures to ensure the bear can coexist in the mountain environment with other animals, including livestock.
It called for better herd protection, secured beehive operations and bear-proof trash cans in the area.
In February 2013, the federal office for the environment authorized the killing in Graubünden of MI3, classified as a “problem bear” after it repeatedly broke into buildings in search of food.
Bears became extinct in Switzerland more than a century ago.
But following a program to reintroduce brown bears to northern Italy from Slovenia 15 years ago, some have wandered into Switzerland on a sporadic basis.
The first of these to be labelled as a nuisance to humans, JJ3, was killed by wildlife officials in 2008.