Twenty of the passengers, believed to be mostly Canadian retirees, were seriously injured, Canwest News Service reported.
The group was traveling from Zermatt towards Austria when the bus driver lost control of the vehicle and left the road near Reckingen, Romandie News reported. Police said the bus fell on its side.
The injured were transported to nearby hospitals by helicopter and ambulance, police said. The identities of the victims had not been released Saturday afternoon.
The bus, which was registered in Germany, was carrying 48 tourists, mostly believed to be Canadian, the driver and a guide, the Canadian Broadcasting Corp. reported.
Swiss police said the road through the Vallee de Conche is not considered especially dangerous.
"It's quite an easy road but it's not very wide," a spokesman, Moulen Pierre-Martin, told CBC.