“No one can get in and out of the hotel to make sure that if other infected people are staying in the hotel, the virus won't be spread,” Interior Minister Karl Nehammer told a press conference.
“All these measures have one purpose — to stop the virus and its spread. There is no reason to panic,” he said, adding that Austria was prepared for such a case.
He did not say how long the isolation would last or identify the hotel, but Austrian media have named it as the 108-room Grand Hotel Europa in the centre of Innsbruck, a tourist hub and push-off point for major Alpine skiing competitions in the surrounding mountains.
The woman's home in Innsbruck — the capital of Tyrol state bordering Italy — was also being isolated, a state government spokeswoman said.
The couple have both been quarantined in a hospital in Innsbruck where they tested positive for the new coronavirus, marking Austria's first cases after an outbreak in northern Italy.
The woman and her partner, both 24 and from coronavirus-hit Lombardy region in Italy, travelled to Innsbruck by car last week.
The woman contacted health authorities after developing a fever, but both are now fever-free again, according Guenter Weiss of the Medical University of Innsbruck.
Earlier Tuesday, Carinthia state, which also borders Italy, indefinitely postponed a cross-country competition, for which 300 participants from northern Italy were expected.
Italy has seen a huge jump in cases in recent days, including 10 deaths. All of those who have died so far in Italy were either elderly or had pre-existing medical conditions.
According to the World Health Organization, the epidemic has peaked at its epicentre in China, where it has killed more than 2,600 people and infected over 77,000 others.