According to BBC, the plane - a Junkers JU-52 HB-HOT - was carrying 17 passengers and three crew on a sightseeing flight when it took off on Saturday afternoon.
It left Locarno Air Base around 16h CET and was heading for the suburbs of Zurich when it crashed at an altitude of 2,540 metres.
All 20 people on board were killed, police said Sunday, Aug. 5, 2018.
Swiss media have been citing plane experts' speculations that the current heat wave may have contributed to the crashes.
JU-Air said on its website that it was "deeply saddened" and its "thoughts were with the passengers, the crew and families and friends of the victims".
The wreckage of the plane was in a basin at 2,450 meters (8,000 feet) above sea level surrounded on three sides by peaks, a Reuters witness said.
Police said all onboard were killed in the crash.
Swiss officials said they are not aware of any distress call from the plane.
There were 11 men and nine women aboard, including an Austrian couple and their son, she said.
Ju-Air said one of its aircraft had been involved in the accident on Saturday.
The area around the crash site, which is popular with hikers and skiers and includes a glacier, was closed to the public.
Officials can essentially rule out a collision with another aircraft or an obstacle such as a wire, Knecht said. Its pilots are ex-military and professional pilots, all of them volunteers.
Ju-Air offers "adventure flights" for people wanting to experience Switzerland's landscape from vintage planes. The airline suspended flights until further notice.