The public prosecutor's office in Salzburg province confirmed the colonel was being investigated for the crime of revealing state secrets.
Austrian Foreign Minister Karin Kneissl said she canceled her visit to Russian Federation scheduled for December 2-3 due to the espionage case.
The Russian Foreign Ministry summoned the Austrian ambassador on Friday to protest over "sensationalist media leak" about a former military officer accused of spying for Moscow, and expressed concern over damage to relations.
The Austrians say they want the Russian to provide "transparent information".
"Recently our Western partners have made it a rule not to use traditional diplomacy, but instead use so-called "megaphone diplomacy" by publicly accusing us and for explanations about matters we know nothing about", Mr Lavrov said.
"Whether this was an isolated case can't be said at the moment", said Kunasek.
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He said the man, whose electronic devices, including a laptop, were being examined, had told investigators that his handlers were interested in weapons systems, recent migration to Austria and information about Austrian personalities.
"Profiles of certain people were also created and passed on", Kunasek said.
"According to our information this activity may have begun in the 1990s and continued until the year 2018", Austrian Chancellor Sebastian Kurz told reporters.
Austria is not a member of North Atlantic Treaty Organisation and sets great store by its status as a neutral country.
"Based on the information we have but also because of recent events for example in the Netherlands we can very much assume at the moment that our suspicion will be confirmed", said Kurz, who has met Putin in Austria twice since the Skripal poisoning.
As such it was one of the few European countries not to expel Russian diplomats following the poisoning of ex-spy Sergei Skripal and his daughter Yulia in Britain in March. Kneissl was criticized by Austria's opposition for inviting Russian President Vladimir Putin to her wedding in August. The FPO has a "co-operation pact" with Russia's governing United Russia party.
A European intelligence agency is understood to have tipped off Vienna about the suspected mole.