Earlier on Saturday, a small plane carrying two parents and their two children crashed in the nearby canton of Nidwalden.
"The JU-Air team is deeply saddened and thinks of the passengers, the crew and families and friends of the victims", the company said in a statement on its website.
Police said that the aircraft had burned and officials haven't yet been able to ascertain the exact number and identity of those who died.
Photos released by Graubuenden canton (state) police showed the crumpled wreckage of the plane lying on the mountain, with only the upside-down tail more or less intact.
The mountainous area in south-eastern Switzerland is popular with hikers and skiers and includes a glacier.
There were 11 men and nine women aboard, including an Austrian couple and their son, she said.
Daniel Knech of the Swiss safety investigation service SESE said the crew did not have time to send out a distress signal.
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The vintage aircraft crashed into the Piz Segnas mountain in the Flims resort on Saturday.
Collision with another aircraft and hitting an obstacle have been ruled out as a potential cause.
The cause of the crash, which occurred hours after a family of four was killed when their small plane went down further west in the Alps, is under investigation.
The company's flight operations were suspended, it said.
The Ju-52 aircraft, made by Germany's Junkers, were made between 1932 and 1952. The JU-Air airline operated three of the vintage planes - decommissioned by the Swiss Air Force and affectionately known as "Auntie Ju" planes - as part of sightseeing tours, Reuters reported.
Chief executive and co-founder Kurt Waldmeier said the planes "are flown exclusively by very experienced professional pilots, and strictly checked and maintained by our own technicians".