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".
There were 11 men and nine women aboard, including an Austrian couple and their son, she said.
Police have given few details but have confirmed the crash, saying the aircraft came down on a mountainside about 2,540m (8,333 ft) above sea level.
"At the moment, no further information is available".
In another crash on Saturday, a family of four including two young children were killed when a small plane came down in central Switzerland.
Based out of Duebendorf in canton Zurich, JU-AIR offers sightseeing, charter and adventure flights with its three midcentury Junkers Ju-52 aircraft, known affectionately in German as "Auntie Ju" planes.
Speaking at a news conference on Sunday in the Alpine resort of Flims, near the crash site, Knecht said the vintage plane presumably didn't have the crash- resistant cockpit voice and data recorders that more modern aircraft have.
Police said on Twitter that five helicopters and a large rescue mission were deployed to the scene of the accident.
Both crashes remain under investigation.
Almost 5,000 Ju-52 planes, a product of Germany's Junkers, were manufactured between 1932 and 1952.
The plane was operated by JU-Air, an association set-up to keep the planes flying after they were taken out of service by the Swiss Air Force in 1981.