The law, passed late Wednesday, also foresees stripping residents with dual nationality of Austrian citizenship if they participate in armed conflicts.
The Team Stronach party and the right-wing Freedom Party argued that the law would not be globally enforceable and is not far-reaching enough.
Niko Alm from the liberal Neos also said the law would prove to be ineffective and that outlawing symbols would only serve to remove them from the public eye.
However, Justice Minister Wolfgang Brandstetter (ÖVP) said that the law was a small but significant step in the fight against jihadism.
The Interior Ministry says nearly 200 people from Austria have left to join the fighting in the Middle East since the Syrian conflict started more than three years ago.