The Austrian authorities had been warned about a possible attack by foreign intelligence services, a Vienna police spokesman, Thomas Keiblinger, told news agency APA.
He said: "There were growing indications of a planned attack in the capital in the past few days."
The suspect was detained at an apartment in Vienna at around 6 p.m. local time (noon ET), Mr Keiblinger said.
He added: "The man has been in custody... There are still lots of things to clear up."
The number of officers on the streets has been increased, while police have also warned people to be alert and tell them if they see any suspicious items.
Police refused to comment on a report from the Kronen-Zeitung newspaper that the suspect had built explosives in Germany.
The newspaper also claimed the man belonged to an Islamist group which originated in Albania, and which held sympathies with Islamic State (ISIS).