Rescue personnel were unable to resuscitate the man, who was severely frozen.
Two others who were caught in the avalanche survived, however.
It is not yet clear what triggered the avalanche, which was described as “gigantic”.
According to local police, the avalanche was unusually powerful. It was around 400 metres wide and 250 metres long.
“We do not know if it was a spontaneous avalanche or if a skier triggered it,” Linda Wasell of Swedish ski resort operator Skistar told news agency TT.
According to Skistar around 9,000 skiers were in the Åre resort area when the avalanche started.
The weather conditions were good and many were skiing in the Tväråvalvet and Stendalen areas, the pistes that are closest to Västerskutan, which is where the avalanche broke out.
Västerskutan is popular among off-piste skiers.
“It is not possible to reach the area where the avalanche started by the lift system,” said Wasell.
When the avalanche broke out at around 1pm on Friday a large rescue operation was launched, with mountain rescue personnel, police officers and others methodically searching the area. A helicopter surveyed the operation from above.
Probes, which are long sticks used in avalanche rescues, were used in the search for the missing man. He was found at around 4.30pm buried under 2.5-metre deep snow masses.
Also on Friday, two skiers were dragged into an avalanche in Hemavan in Västerbotten, northern Sweden. No one got caught under the snow there.
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