Local authorities are still searching for a sixth person.
A huge search and rescue operation was launched on Saturday after the group went missing near the 3,706m high Tete Blanche mountain.
They had set off from Zermatt, home of the famous Matterhorn mountain, on a ski tour towards Arolla along the Swiss-Italian border.
Five of the six skiers were found at 21:20 local time (20:20 GMT) "without any signs of life," a statement from Swiss Valais canton police said.
Authorities had previously told the BBC that the skiers were all Swiss nationals, and range in age from 21 to 58 years old.
Local police said teams on both sides of the route were alerted but severe weather was hampering the operation.
There have been high winds in the Alps for some days, and over the past 24 hours, heavy snowfalls. Saas-Fee, a winter resort neighbouring Zermatt, is currently cut off by snow.
Anjan Truffer, the head of Zermatt's air rescue service, told the BBC that the weather was so bad that "flying is not an option", with "very strong winds, heavy snow, high avalanche danger, and zero visibility".
Mr Truffer said that the group may have been overcome by the bad weather, rather than struck by an avalanche, because they went missing on a part of the Zermatt Arolla route where the risk of avalanche is low.
Ski tours typically follow unprepared alpine routes, and are usually equipped with location finders and avalanche shovels.
The last signal from the group was recorded overnight. It was "not verbal", Mr Truffer said, but allowed rescue services to get a rough idea of their location.
The route from Zermatt to Arolla is part of the famous 120km (75 miles) "Haute Route" from Zermatt to Chamonix.
It is very popular, but suitable only for the most experienced skiers, and can take several days.
Additional reporting by Sofia Ferreira Santos
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