Interior Minister Guenther Platter told a press conference that the two men, aged 20 and 26, and a 21-year-old woman were "in contact with al-Qaeda networks" but did not form an "operational group" planning violence.
Public security chief, Erich Buxbaum, said the three, all resident in Vienna, were second generation Austrian Muslims whose families came from the Arab world.
Police said searches were also being carried out following the arrests in the Austrian capital.
Islamist militants threatened to attack Germany and Austria if they do not pull their troops out of Afghanistan in a statement read out on March 11 by a masked man on a website linked to al-Qaeda.
"In standing by the United States… you have provoked those whom you call terrorists to target you," the man said in Arabic, with a German translation appearing on the screen as the flags of Germany and Austria appeared in front of a burning background.
Addressing the government in Vienna, the statement said: "Don't destroy the security of a whole country just for five soldiers you have sent to Afghanistan."
The two governments sought to play down the threat at the time, with Austrian Chancellor Alfred Gusenbauer saying: "People have no reason to worry."
Austria has four staff officers with the International Security Assistance Force backing the Kabul government, whose mission is to end on December 31.
In March minister Platter ruled out ending that mission, adding that Austria was not a "primary target for terrorists."
German Interior Minister Wolfgang Schaeuble for his part said Berlin "will not be blackmailed" into withdrawing its some 3,000 troops from Afghanistan.
The Voice of the Caliphate was launched in September 2005 by the Iraqi branch of the al-Qaeda network of the Western world's most wanted man, Osama bin Laden.