The Austrian chancellor and defense minister said the case came to light as a result of information from another European intelligence agency.
Relations between Russia and the West were plunged in new controversy on Friday as Austria placed a senior officer in its own military under investigation on suspicion of spying for Moscow.
The suspect, a 70-year-old retired colonel in the Austrian army who has not been named, is alleged to have passed secrets to Russian intelligence for 20 years in return for payments of €300,000 (£260,000).
“Russian spying in Europe is unacceptable and must be condemned,” Sebastian Kurz, the Austrian chancellor, told a hastily assembled press conference in Vienna on Friday.
“Of course, if such cases are confirmed, it will not improve relations between Russia and the European Union.”
Russia denied all knowledge of the case and accused Austria of conducting “megaphone diplomacy”.
The suspect is believed to have been recruited by Russian intelligence in the 1990s, and passed information about weapons systems and key individuals to Moscow.
Although he retired from the military five years ago, he is believed to have continued to spy until earlier this year.
“We are demanding transparent information from the Russian side, and will discuss the way forward with our EU partners,” Mr Kurz said.
Austria was alerted to the case by a tip-off from an allied intelligence agency, Mario Kunasek, the defence minister said.
Although officials have refused to comment on the identity of the intelligence agency involved, Austria’s Der Standard newspaper reported the warning came from Germany.
“We can’t say for the moment whether this is an isolated incident or not,” Mr Kunasek said.
The suspected officer told interrogators Russia had asked him for information on weapons systems and the migration situation in Austria, he said.
“Profiles of certain people were also created and passed on,” he said.
Russia supplied the colonel with an encrypted device, according to Austrian press reports. He also met regularly with a contact named only as “Yuri”, usually abroad