"The police have the sad certainty that the 20 people aboard perished", police spokeswoman Anita Senti told a news conference.
It crashed about 2,540m (8,333 ft) above sea level, on the western side of a 3,000m peak called Piz Segnas.
Police had not provided an official toll by late Sunday morning, but said that five helicopters were involved in a search and rescue mission and the airspace over the crash site was to remain closed until late Sunday. Most of the victims were Swiss but they also included a couple and their son from Austria.
All 17 passengers and three crew members died in the crash, which happened around 5 p.m. local time.
Knecht said officials expect the investigation of the cause to be "relatively complex, because we have to compare various indications, information and evidence and evaluate them".
The mountainous area in southeastern Switzerland is popular with hikers and skiers and includes a glacier.
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The Junker JU52 HB-HOT aircraft, built in Germany in 1939 and now a collectors item, belongs to JU-Air, a company with links to the Swiss air force, the ATS news agency 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".
"We can not yet explain what led to the tragic accident on Piz Segnas", he said.
Operator JU-Air has now suspended all flights until further notice.
JU-Air runs sightseeing tours on its squadron of German-made vintage aircraft.