The plane went down 3,300 metres (10,800 feet) above sea level at 4:45 pm (1445 GMT) on Friday in an area known as the Dunand Pass, police in southern Valais canton said in a statement.
They identified the plane as a four-seater made by the French firm Robin and which had taken off from Sion airport for "a pleasure flight".
After receiving an alert, authorities dispatched rescue teams to the summit but found the pilot and three passengers dead at the scene.
"The circumstances of the accident have not yet been determined," police added. The victims have not yet been formally identified.
The accident comes after an unusually deadly winterseason in the Swiss Alps that saw multiple hikers killed in a series of avalanches.
A glacial lake in Valais, Switzerland. Photo: Grindl1/Wikicommons