Mr. Firtash has strong connections to the ousted Ukrainian president, Viktor F. Yanukovych, and also conducts extensive business in natural gas with Russia.
The Austrian federal police identified the man only as Dmitry F., a 48-year-old Ukrainian citizen, and said he was arrested Wednesday evening in a district of Vienna without incident.
A government source confirmed that it was Mr. Firtash.
The F.B.I. has been investigating Mr. Firtash since 2006, and an arrest warrant had been issued for him by a federal judge in Virginia, the Austrian authorities said.
The arrest comes amid political turmoil in Ukraine, with Russian forces occupying the Crimean peninsula in the south and regional officials there seeking to break away from Ukraine to become part of Russia.
In a statement, Mr. Firtash’s main company, Group DF, confirmed his arrest but called it a “misunderstanding” with no connection to the unrest in Ukraine.
The company said the action in Austria was “related to an investment project dated 2006.”
The United States has begun to impose sanctions on Russia in response to its intervention in Ukraine.
On Wednesday, President Obama met at the White House with Ukraine’s acting prime minister, Arseniy P. Yatsenyuk, in a show of support for the fledgling government that has replaced Mr. Yanukovych.
In a twist, Mr. Yatsenyuk, a veteran of Ukrainian politics, has also been accused of close ties to Mr. Firtash.
The former prime minister Yulia V. Tymoshenko, now an ally of Mr. Yatsenyuk, had once derided him as a “political project” of Mr. Firtash.
Ms. Tymoshenko and Mr. Yatsenyuk both ran for president of Ukraine in 2010, with Ms. Tymoshenko losing in a close race to Mr. Yanukovych while Mr. Yatsenyuk received less than 7 percent of the vote.
Mr. Firtash, who made his fortune in natural gas, developed a close business partnership with Sergey Levochkin, who served as the chief of staff of Mr. Yanukovych’s presidential administration.
Together, Mr. Firtash and Mr. Levochkin last year purchased Inter Media Group, a media and broadcasting company that includes the popular Inter television station.
Group DF, Mr. Firtash’s company, is a conglomerate that includes chemical manufacturing companies, energy transport and supply firms, and banks and media outlets in addition to the Inter group.
Forbes Ukraine has pegged his net worth at $673 million, though his actual wealth is believed to be in the billions.
Mr. Levochkin submitted a resignation to Mr. Yanukovych shortly after the start of the antigovernment protests in Kiev in late November, but Mr. Yanukovych refused to accept it.
Mr. Levochkin left the administration earlier this year, though it was unclear at the time if he had been dismissed or had quit.
Since Mr. Yanukovych’s ouster late last month, some European countries, including Austria, have said that they were looking to freeze assets tied to him.
He is wanted in Ukraine on charges of mass murder.
Source: The New York Times