The law has been widely referred to as a "burka ban" and is seen by many as targeting the full face coverings worn by conservative Muslim women.
But one of the first people to allegedly violate the law was not a Muslim woman, but rather a man wearing a face-covering shark outfit to promote a McShark computer store in Vienna.
Violators of the law can be fined 150 pounds, the equivalent of about $176.
The managing director of the advertising agency behind the campaign, Eugen Prosquill, reportedly told the Vienna newspaper Heute he didn't know the new law also applied to characters in costumes.
"It would be a pity if there were no mascots left," he told the newspaper.