The army said an officer spotted the two Belgian Shepherd dogs running loose at the barracks south of Vienna early Thursday. The fatally injured staff sergeant was subsequently found inside the dogs' kennel.
An investigation has been launched into the cause of the attack.
Austrian public broadcaster ORF quoted a Defense Ministry spokesman saying one of the dogs was an fully trained service dog while the second, aged about six months, was about to undergo training.
Austrian President Alexander Van der Bellen has expressed his condolences to the victim's family and to his fellow soldiers.
The Austrian army has 170 service dogs.
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