The man, 24, was already sick before his arrival in Austria and was therefore part of a high-risk group, the regional health director for Salzburg, Christoph Koenig, told ORF public television.
Officials in the German state of Lower Saxony on Monday announced the A/H1N1 virus had killed a three-year-old girl and a 51-year-old man in Göttingen. They said there had been a spike in infections in Germany in the past month.
The World Health Organisation declared the swine flu pandemic over in August, more than a year after the virus that emerged from Mexico sparked panic and killed thousands of people around the world before fizzling out.
An estimated 250 people have died from swine flu in Germany since the virus emerged in 2009.