The accident happened late on Friday when around 650 people were celebrating inside the tent in Sankt Johann am Walde in the north of the country.
"(The) extreme storm tore away most of the tent," a statement said. "The two people were killed by flying debris including the tent scaffolding."
Those killed were a 19-year-old woman and a 28-year-old man, both from the local area.
Storms barrelling through Austria on Friday night caused widespread havoc elsewhere, temporarily cutting off power to 150,000 households with winds of up to 126 kilometres (78 miles) per hour.
Two people were hurt in Salzburg by falling pieces of scaffolding while elsewhere flying objects and falling trees caused numerous car accidents and blocked train lines.
In the historic central spa town of Bad Ischl, a circus tent was destroyed, giving a taste of freedom to a number of performing goats and ponies that briefly escaped.