Police spokeswoman Anita Senti told reporters that it was with "sad certainty" that "the 20 people aboard perished".
Police said on Twitter that five helicopters and a large rescue mission were deployed to the scene of the accident, which occurred on the west side of the Piz Segnas mountain in the canton of Graubuenden.
Police said they are not aware of any distress call from the aircraft before it crashed.
Officials said 11 men and nine women were killed, most from Switzerland but also a couple and their son from Austria.
According to German-language newspaper Blick, the flight had taken off from Ticino in the south of the country and had been due to land at the Duebendorf military airfield near Zurich on Saturday afternoon.
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Local media and aviation websites have reported that the plane, which seated 17 passengers along with two pilots and a flight attendant, was fully booked and that no one survived.
JU-Air says it runs a small fleet of four Junker planes, all built in 1939, which are for hire.
Both crashes remain under investigation.
Earlier on Saturday, a small plane crashed in the Rengg mountain pass area in the canton of Nidwalden, killing two parents and their two children.
There are now no details on casualties but the Ju-52 can carry up to 17 passengers, two passengers and a flght attendant.