"Our police forces managed in quick time to arrest a suspect and so prevent a potential terror attack in the federal capital Vienna," Wolfgang Sobotka said shortly after police in the capital announced the arrest.
"The suspect is an Austrian citizen with a migrant background who is 18 years old," Sobotka told a news conference. He said that possible indications that he may be an Islamic extremist were being looked into.
"There are individual indications (of extremism) that we have to investigate. There is one contact that is pretty clear and there are several indications that will be looked at intensively," Sobotka said.
A police spokeswoman told AFP that signs had multiplied in "recent days" that there might be an attack in the city, which is popular with foreign tourists, and that security measures had been increased.
"The presence of uniformed and plainclothes police was increased and today at 1800 (1700 GMT) the suspect was arrested in Vienna near his address," spokeswoman Irina Steier said.
Sobotka said that the man, who lived in Vienna, had been under observation for several days and that he did not resist arrest. He said that "decisive" information came from foreign intelligence agencies.
Austria spared so far
Police also issued a public warning for people to be on the lookout at crowded public places and to inform police if they see any suspicious objects.
Austria has been spared in the string of attacks by Islamist extremists in recent years suffered by other European countries.
In 2015 a record 90,000 people applied for asylum in Austria after hundreds of thousands of migrants transited the country bound for Germany and elsewhere.
Several of the attackers behind the November 2015 deadly attacks in Paris transited through Austria with false papers among the flow of migrants.
In December 2015, two migrants were arrested in Salzburg and later extradited to France over their alleged intent to take part in those attacks, which left 130 people dead.
A Moroccan asylum-seeker was detained in Austria in December for allegedly planning an attack in Salzburg over the Christmas and New Year period, prosecutors said.
The 25-year-old was arrested in a refugee centre in a small Alpine resort town near Salzburg in western Austria, close to the German border.
"Today's case shows once again that Austria is no blessed isle. That Austria, like Europe, has to expect terror situations," Sobotka said.
Austria's opposition far-right has risen in popularity by stoking concerns about immigrants, coming close in 2016 to winning the largely ceremonial but coveted presidency and leading national opinion polls.
In the latest arrest, the Kronen-Zeitung newspaper published online a document from the BVT anti-terrorism agency saying that a group of "radical Islamists of Albanian origin" intended to launch an attack in Vienna.
It said that according to information from a foreign intelligence agency and, independently from a foreign police force, the attack was to take place between January 15 and January 30.
The document, whose veracity could not be confirmed, added that a German-speaking sympathiser of the Islamic State (IS) extremist group made explosives in Germany and that he intended to bring them to Vienna to carry
out an attack.