The avalanche, estimated to have been 300 metres (nearly 1,000 feet) wide and 600 metres long, happened near the Mittelallalin summit, home to the world's highest revolving restaurant, police in the southern Swiss canton of Valais said in a statement.
The six off-piste skiers had been skiing from the Mittelallalin region towards Saas-Almagell.
Four of them managed to pull themselves out and were unharmed.
But a 36-year-old man from Valais was airlifted to hospital in Bern where he died of his injuries, and a 49-year-old man from the same region was injured and flown to a hospital in nearby Visp.
The accident is the latest in a series of deadly avalanches across the Alps.
Last month, two Italian cross-country skiers were killed in another snowslide in Valais.
Most of the accidents this season have meanwhile been on the French side of the border, where at least 15 people have died in avalanches, including six members of the French Foreign Legion who were swept away last month during a training exercise.
Five Czech skiers were also killed earlier this month in an avalanche in the Austrian Alps.
AVALANCHE
Off-piste skiers hit by deadly avalanche
One person was killed and another injured on Sunday when an avalanche in the Swiss Alps swept away six off-piste skiers, police said.
SKI
Dad’s ‘miracle escape’ after being buried by avalanche in French Alps
A man out walking with his family in the French Alps has made a miraculous escape from an avalanche after spending more than two and a half hours trapped under snow, rescuers said.
The 50-year-old father was snowshoeing near the high-altitude Val d'Isere ski resort with his wife and two children on Thursday without anti-avalanche safety equipment.
“Thank to the mobilisation of nearly 100 people… the man was found alive after two hours and 40 minutes of searching,” the police for the local Savoie département announced on Twitter.
Because of the depth of the snow, rescue dogs were unable to detect a trace, but the man was eventually dug out by a specialised mountain police team which used a Wolfhound device to locate his mobile phone under the ice.
“I think it's a miracle,” Alexandre Grether from the PGHM rescue team told the France 3 local news channel, adding that the man was found 2.5 metres (eight feet) below the surface.
The chances of survival after more than 20 minutes in an avalanche are usually slim.
“He was protected by a tree, that's what prevented him from being crushed by all the ice that slid down. The snow had surrounded him, but he had a pocket of air,” he explained.
The victim is expected to make a full recovery after suffering a fracture to his hip.
The avalanche risk on Thursday was at its maximum – five on a scale of five – and rescuers urge people to always check the snow conditions before venturing out.
READ ALSO 'Whole season a write-off' – what next for France's ski resorts?
Ski lifts in the Alps, which have seen some of their heaviest snowfalls in years in January, are currently closed because of restrictions imposed by the government to limit the spread of Covid-19.
Visitors and locals are free to enjoy hiking, cross-country skiing and snow-shoeing, but occupancy levels in hotels and chalets are way down and business owners and seasonal staff face serious hardships.
The government has promised an economic support package for the sector.
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