The man from Vienna had been snowboarding with two other people in open terrain, and may have inadvertently started the avalanche, police said.
He was buried under the cascading snow but his companions were able to dig him out and he was taken to hospital by a mountain rescue team.
Meanwhile in Tyrol a mountain rescue team and alpine police are searching for a German hiker who has been missing since Saturday afternoon.
The 42-year-old was climbing the Pleisenspitze mountain (2,569 metres) when he told others in his group that he was going to make his way back down to the valley, but he never arrived at an agreed meeting point. An initial search had to be called off due to a snowstorm on Saturday evening.
Avalanche experts in Tyrol have said there is considerable danger of slides above 2,000 metres and warned skiers to be especially careful around fresh snow drifts in the Arlberg region, Außerfern, the Northern Alps and the Kitzbühel Alps.
In the past few days the area around Innsbruck has seen 40 centimetres of fresh snow, and the rest of Tyrol around ten centimetres.