"The police have the sad certainty that the 20 passengers perished", said a spokesperson for regional police in the canton of Grisons.
The incident happened yesterday when the plane crashed in a basin at 2,450m above sea level on the west side of the Piz Segnas mountain shortly before 5pm local time.
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. Most of the people killed were from Switzerland, along with an Austrian couple and their son. Their names were not released.
The vintage aircraft crashed into the Piz Segnas mountain in the Flims resort on Saturday.
The wreckage was discovered engulfed in flames, and the cause of the crash is now being investigated by the Federal Prosecutor's Office, in cooperation with local Swiss authorities. There also was no indication of any "external influence", he said, indicating that authorities don't suspect foul play.
An eyewitness told Swiss newspaper 20 Minutes that the "plane turned 180 degrees to the south and fell to the ground like a stone".
The mountainous area in south-eastern Switzerland is popular with hikers and skiers and includes a glacier.
Video shows man taunting bison at Yellowstone National Park
Reinke was issued a citation requiring a court appearance that same evening before the park was aware of the circulating video. These distances safeguard both visitors and the experience of sharing a landscape with thousands of freely-roaming animals.
The cause of the crash is not known.
Ju-52 planes were manufactured between 1932 and 1952 and can carry 17 passengers and three crew members.
The Junker JU52 HB-HOT aircraft was built in Germany in 1939 and is now a collectors' item. Its pilots are ex-military and professional pilots, all of them volunteers.
The company's flight operations were suspended, it said.
"Yesterday was the worst day in the 36-year history of JU-Air", the airline's Chief Executive Kurt Waldmeier said at a news conference in nearby Flims on Sunday.
The aircraft have three engines, one on the nose and one on each wing.
JU-Air runs sightseeing tours on its squadron of German-made vintage aircraft.