The incident occurred at around 11am when a group of five mountaineering skiers were heading down the north slope of the Pointes de Tsavolire, a 3,026-metre mountain, Valais cantonal police said in a statement.
The avalanche carried away four of the skiers, the statement said.
The fifth skier was able to dig out two of them, who were slightly injured, police said.
Emergency rescue workers from the Maison du Sauvetage and Air Glaciers found the other two, buried beneath more than 2.5 metres of snow.
They were transported by helicopter separately to hospitals in Lausanne and Sion for treatment of critical injuries, police said.
Marcel Délèze, guardian of the Becs de Bosson mountain hut, told local newspaper Le Nouvelliste, that the skiers were members of the CERN ski club.
He said they had earlier left the village of Eison in the Val d’Hérens.
Police said they were heading toward another valley, the Vallon de Réchy, south of Sierre, when the avalanche struck.
“In seeing that a sheet (of snow) had let go on this face, I called for help and then went to the site with people present in the hut,” Délèze said.
“We localized the skiers before the emergency services arrived but some were under three metres of snow,” he told Le Nouvelliste.
“To free them took a lot of time.”
The ages of the victims, reportedly Swiss citizens, were not disclosed.
Elsewhere, in the canton of Schwyz, a 31-year-old man died after falling 100 metres while hiking in steep terrain on the Rigi-Hochflue, a steep mountain overlooking Lake Lucerne near Lauerz, police said.
Other hikers discovered the man, a resident of the canton of Zug, in a seriously injured condition on Sunday around noon.
He was transported by helicopter to hospital where he died in the afternoon, Schwyz cantonal police said.