Reports in the Austrian media said 500 police were involved in searches at mosques, flats and prayer rooms in Vienna and the cities of Linz and Graz.
Authorities also seized “terrorist propaganda material”, prosecutors said.
It comes amid a European crackdown on fighters who have joined jihadist forces in Syria and Iraq.
A statement from Austria’s state prosecutor’s office said 16 people had been questioned following the searches in the early hours of Friday.
The 13 suspects had been arrested on suspicion of membership of a terrorist organisation.
Local media said a Bosnian preacher, who was the main suspect, was among those held.
Along with “propaganda material”, officers seized electronic material, cash and a brass knuckles, according to reports.
Hundreds of European Muslims are known to have travelled to Syria to join jihadist groups such as Islamic State fighting in the country’s civil war.
EU member states are trying to prevent radicalisation at home and are also taking measures to tackle the security threat from jihadists returning from Syria. (BBC)
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