Special police units and local police forces were alerted by a caller who said several people were lying wounded on the ground at about 8:50 p.m. (1950 GMT), the police statement said.
It said the incident was being investigated and the site had been closed off. More information would be released later today at a news conference in the village, which is close to the town of Sion, the capital of the canton - or region - of Valais.
Mass shootings are rare in Switzerland, although gun possession is widespread - some estimates run to at least one for every three of its 8 million inhabitants. Many are stored in people's attics, a legacy of Switzerland's policy of arming its men to defend its neutrality.
More top news
Rock band Radiohead return with a new song, having deleted most of their social content in the last few days.
Kandyce Downer had been made the legal guardian of toddler Keegan, who was found to have sustained more than 150 injuries.
Disneyland have announced a new wedding venue in the Magical Kingdom - the beautiful East Plaza, with stunning views of Cinderella castle.