The man, who teaches at a school for ten to 14-year-olds, reportedly told his students that it is acceptable to hurt somebody if they have offended Allah.
The school board told the Austrian Press Agency (APA) that his students also said that he told them in a conversation outside of school that he considered killing someone to be a legitimate form of punishment for insulting Islam.
His students reported him to social workers and the school principal.
The case has been handed over to the Federal Office for the Protection of the Constitution and Counterterrorism (BVT). If the allegations are confirmed the man will be banned from teaching, the president of the school board told APA.