The suspect, whom it also did not name, "was in contact with diplomats and intelligence officials from various countries and was in Moscow shortly before and during the military invasion of Ukraine by Russian forces", the statement said.
The suspect, who faces up to five years in prison for "supporting a secret intelligence agency to the detriment of Austria", is not being remanded in custody, it said, adding that undefined further steps would be taken by the justice system.
It provided no further information about his father.
The ministry described the suspect's role as reporting on what was generally being discussed in Vienna, renowned since the Cold War as a den of spies.
"It is suspected that he was used as a source of information on discourse among the Austrian population, the country and the press relating to foreign policy, society as a whole and security policy and was therefore brought to Moscow in the run-up to the military operation to assess possible foreign reactions," the ministry said.