Daniel Knech of the Swiss safety investigation service SESE said the crew did not have time to send out a distress signal.
"The police have the sad certainty that the 20 people aboard perished", police spokeswoman Anita Senti told a news conference.
The wreckage of the plane was in a basin at 2,450 metres (8,000 feet) above sea level surrounded on three sides by peaks, a Reuters witness said.
Police in central Switzerland said that a small plane has crashed in a forest, killing several people.
He and senior police official Andreas Tobler said the vintage plane lacked "black boxes", the crash-resistant cockpit voice and data recorders that more modern aircraft have.
Almost 5,000 Ju-52 planes, a product of Germany's Junkers, were manufactured between 1932 and 1952.
The airspace above the crash site was closed by the Federal Office for Civil Aviation and access to popular hiking trails in the surrounding area was blocked. They also expect the investigation into the cause of the crash to be "relatively complex".
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The Ju-52 aircraft, made by Germany's Junkers, were made between 1932 and 1952.
According to the SwissInfo website, citing local police, the plane went down near the Piz Segnas mountain on the afternoon of August 4 at an altitude of 8,330 feet. The operator said it was saddened by the news and it had set up a helpline for relatives. Its pilots are ex-military and professional pilots, all of them volunteers.
The aircraft have three engines, one on the nose and one on each wing.
"We can not yet explain what led to the tragic accident on Piz Segnas", he said.
Based out of Duebendorf in canton Zurich, JU-AIR offers sightseeing and adventure flights around the Alps.
A brochure on the company's website listed the cost of the 2-day Locarno trip as 1,130 francs ($1,136), including meals and a night in a hotel. It has suspended all flights until further notice.