Mr Firtash, one of Ukraine's richest men, is wanted by US authorities on suspicion of corruption and forming a criminal organisation.
The 48-year-old was regarded one of the main backers of the ousted Ukrainian President, Viktor Yanukovych.
Austrian police said the arrest was not related to current political events in Ukraine.
"A national arrest order was issued for the businessman on the basis of several years of investigation by the US FBI and an arrest warrant," a police statement said.
He was arrested in an area  of Vienna where one of his businesses was registered, Austrian media say.
Mr Firtash is founder and chairman of Group DF, whose website describes it as an international group of companies operating across Europe and Asia in energy and banking.
He also has many interests in petrochemicals and media.
Mr Firtash was a powerful voice in Ukraine's economic policy circles under former President Yanukovych, who was ousted by pro-European protesters last month.
Much of the anger behind the protests was fuelled by perceptions of corruption, and the alleged close links between the government and oligarchs.
Mr Firtash is not named on an initial EU list of Ukrainians suspected of misusing state funds and violating human rights, and whose assets are to be frozen as a result of the crisis over the Russian takeover of Ukraine's Crimea region.
Ukrainian gas tycoon Dmytro Firtash has been arrested in the Austrian capital, Vienna, police say.