The incident occurred on Saturday afternoon as the woman was descending the mountain with a group of six other people, police said in a news release.
As the group headed toward a hut located at an altitude of 2,480 metres on the south slopes of the Grand Muveran, the victim stumbled and lost her balance.
She fell about 200 metres down a rocky slope.
An emergency services doctor from Air Glaciers, arriving at the scene by helicopter, found the woman was already dead.
The victim was a resident of the canton of Bern.
The Grand Muveran is a 3,051-metre tall mountain located on the border of the cantons of Vaud and Valais.