The skiers, five of them members of the same family, went missing around Tete Blanche mountain on March 9 on the Zermatt-Arolla path, near the Matterhorn mountain that straddles the border between Switzerland and Italy, Reuters reported.
The bodies were discovered on March 10 in Tête Blanche sector, police said.
The skiers were between the ages of 21 and 58, according to an earlier police statement.
Five belonged to one family from the Valais canton, while a sixth person is from the canton of Fribourg.
Police did not reveal the identity of those who were found dead.
Zermatt is a popular mountain resort renowned for skiing and attracts tourists from around the world.