The hunter spotted the bear on Thursday morning, alerting authorities who in turn warned local farmers, reported newspaper 20 Minutes.
The Graubünden office of hunting and fishing advised the owners of livestock in the area to bring their herds close to mountain buildings during the night, in case of attack.
However Nicola De Tann, head gamekeeper in the Moesa region, told news agency ATS that the bear shied away when it saw a human.
“It's a good sign. This bear is visibly frightened by people. So the risk of this big predator approaching residential areas is slim.”
Val Mesolcina hasn't had any bears since the animal was hunted to extinction in the area in 1904.
However the canton as a whole has experienced more recent bear visits, which often do not end well.
A two-year-old bear named M25 provoked debate during the summer of 2014 after killing several sheep and donkeys in the Val Poschiavo, leading to a WWF petition calling on the cantonal authorities to protect the animal from being shot.
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 a programme aimed at reintroducing brown bears to northern Italy means some do wander 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.