Kurz told a press conference that the colonel is suspected to have begun working with Russian intelligence in the 1990s and carried on until 2018.
Foreign Minister Karin Kneissl has summoned the Russian charge d'affaires over the matter and cancelled an upcoming trip to Russia, Kurz added.
"Of course if such cases are confirmed, whether it be in the Netherlands or in Austria, it can't improve the relationship between the EU and Russia," Kurz said.
He was referring to the expulsion of four Russian agents by the Netherlands in April for allegedly planning a cyber-attack on the world's chemical weapons watchdog in The Hague.
"Russian spying in Europe is unacceptable and to be condemned," Kurz added.
Austrian Defence Minister Mario Kunasek told the press conference that the case came to light "a few weeks ago" as a result of information from another European intelligence agency.