The area, which includes a glacier, is popular with hikers.
Authorities are investigating what caused the deadly crash.
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.
Junkers JU-52 planes were manufactured between the 1930s and 1950s.
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".
"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 company's flight operations were suspended, it said.
The aircraft have three engines, one on the nose and one on each wing.
The company did not offer any further information.