Max Zirngast, a journalist with the far-left magazine Re:volt in Germany, was arrested in Ankara at dawn on Tuesday, according to the publication, which added that he was facing "terrorism" charges.
"The Austrian government calls on the Turkish government to present the reasons for the arrest or to immediately release the journalist," Austrian government spokesman Peter Launsky-Tieffenthal said on Twitter.
"Austria stands unconditionally for freedom of conscience and of the press. The Austrian citizen arrested in Turkey today is receiving consular assistance from the Austrian embassy," he added.
Press watchdog Reporters without Borders (RSF) had also called for Zirngast's immediate release.
Zirngast had published articles on the outlawed Kurdistan Workers Party (PKK), which has waged a Kurdish insurgency inside Turkey since 1984.
It is blacklisted as a terror organisation by Ankara and its Western allies.
"Divergent political opinions are no justification for arrests and intimidation, which are happening more and more in Turkey," Reporters without Borders in Austria said in a statement.
Rights organisations have frequently criticised Turkey for its violations of press freedom, which have stepped up since a failed coup attempt in July 2016.
Turkey ranked 157 out of 180 countries in the 2018 World Press Freedom index published by RSF.