According to the Kurier newspaper, the incident took place on late Thursday, with the young Turks kicking benches and a confessional, as well as shouting "Allahu Akbar!"
A priest called the police but the assaulters had left the site before the officers arrived. The regional department of the Office for the Protection of the Constitution and Counterterrorism believes that the group of radical Turkish extremists, which is operating in the area, is behind the incident.
Both Interior Minister Karl Nehammer and Chancellor Sebastian Kurz have condemned the incident.
"All Christians must have a right to freely and safely practice their faith in Austria! We will firmly continue the fight against political Islam and refrain from false tolerance here", Kurz wrote on his Twitter page.
Commenting on the recent terrorist attack in France's Nice, which claimed the lives of three people, Nehammer said that "every terrorist attack is an attack on our democracy and our European fundamental and freedom rights".
Europe has been facing a spike in the incidents related to radical Islam since the brutal beheading of a French history teacher by a radicalised teen in Paris and the tough rhetoric of French President Emmanuel Macron following this attack.