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
Theresa May could face a Tory rebellion as MPs demand to see her plan for Brexit.
"I've never told anyone that before," she told the Today Show on a visit to a homeless shelter in New York.
Find out where the year's political shocks and England's football failure rank, plus the UK's most followed celeb and most talked about TV.