The 77-year-old was on her way to the Grauberg gondola station from the Nagens mountain restaurant on Friday when she took a path through the alpine pasture, police said on Saturday.
After passing through the electric fence, she was attacked by cows grazing on and around the trail, who knocked the woman to the ground and trampled over her.
A cyclist witnessed the scene and called air ambulance Rega, but the woman died at the scene from her injuries, despite attempts to resuscitate her.
According to Germany's DPA news agency, the woman was a German tourist from Berlin.
Hikers often encounter cattle on paths throughout the Swiss Alps.
Attacks are rare but do occur, especially when the herd contains calves.
Last year a family of tourists were attacked by a cow with a calf above Davos, also in Graubünden.
In 2012 a woman was attacked by cows in a pasture above Saint-Gingolph in the canton of Valais.
Speaking to Swiss radio, Walter Grass, president of the Association of Graubünden walking trails (BWA), called for action to prevent future incidents, reported newspaper Neue Zürcher Zeitung on Monday.
In a letter to municipalities, the association asked them to check the safety of their trails and seek a dialogue with farmers over the issue.
The problem can only be avoided entirely if footpaths are diverted or completely fenced off, the paper reported.
Hikers are advised to keep dogs on leads, keep a good distance from cows and not turn their backs to them.
“Threatening behaviour is characterized by the lifting and lowering of the head, snorting, pawing and roaring,” said Grass.
“If you notice these alarm bells, slowly leave the pasture backwards. Fast movements are threatening to cows.”