The state prosecutor has confirmed that the arrest happened on Monday, according to a report in the news magazine Profil.
Police spokesman Hans Jörg Bacher said a 41-year-old Imam of Chechen origin was taken to Graz-Jakomini prison on Wednesday. The investigating judge is due to decide today whether the man should be released before trial.
His arrest followed two police searches in places of Muslim worship in late April, during which documents and media were confiscated, which implicated the cleric.
According to the Profil report the man is alleged to have been involved in radicalising at least eight young Chechens living in Styria, and persuaded them to fight in Syria.
Four of these men, who joined the Al-Nusra Front (a branch of Al-Qaeda operating in Syria), are already dead. The Al-Nusra Front is classified as a terrorist organization by the UN Security Council.
Mehdi Nemmouche, the Frenchman being held over a fatal shooting at the Jewish Museum in Brussels, is also connected to the Al-Nusra Front, according to Profil.
Austria is considering withdrawing Austrian citizenship or asylum status from people who go to fight in Syria or other foreign wars, so long as they have an alternative nationality they can assume.