Eleven men and nine women were killed, officials said. It was flying a group of 14 Swiss nationals and a three-member family from Austria on a sightseeing tour for the company JU-AIR.
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. They also expect the investigation into the cause of the crash to be "relatively complex".
"Based on the situation at the crash site we can say that the aircraft smashed into ground nearly vertically at relatively high speed", said Daniel Knecht of the Swiss Transportation Safety Investigation Board.
A plane crashed on the Piz Segnas mountain.
Collision with another aircraft and hitting an obstacle have been ruled out as a potential cause. There also was no indication of any "external influence", he said, indicating that authorities don't suspect foul play.
The plane, which was built in Germany in 1939, crashed into the Piz Segnas mountain around 2,450 metres (8,000ft) above sea level.
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. Knecht said that while heat can affect an aircraft's performance, experienced pilots could deal with that.
The company's flight operations were suspended, it said. He said it had its full annual service during the winter, and "we know of no technical problems with this aircraft".
The incident was the worst in Switzerland for several years, but just one of three plane crashes in the country in the space of eight days.
"We can not yet explain what led to the tragic accident on Piz Segnas", he said.
The aircraft was in possession of JU-Air, a company with links to the Swiss Air Force.
It said it was suspending flights until further notice.