The Kurier, a popular daily, said an Austrian Air Force officer who allegedly passed on classified information to the Russian spy, had also been detained following a lengthy surveillance operation conducted by Austrian military counterintelligence.
The information was later confirmed by an official spokesman for the Austrian Prosecutor General's office.
"I can only confirm that a Russian citizen and an Austrian officer have been arrested," the official told RIA Novosti.
According to the newspaper, the Austrian suspect, who served as a technician in the Austrian Air Force and had many contacts with civilian firms in Germany, could have supplied the Russian spy with research data in electronics.
Austrian authorities have not revealed the identities of the alleged spies, in the interests of the investigation.
The Russian Embassy in Vienna did not comment on the article in the Austrian newspaper, but a senior embassy official told RIA Novosti that "Russia has sent a protest note to the Austrian Foreign Ministry in connection with the arrest of a member of an official Russian delegation participating in a meeting of the UN Committee on the Peaceful Uses of Outer Space."