"The shark was fined because he refused to take his mask off", police spokesman Daniel Fürst told Heute newspaper.
Violators of the law can be fined 150 pounds, the equivalent of about $176.
The worker had donned a furry suit with a shark's head for a hat to advertise the opening of a branch of computer store McShark in Vienna. "Although it's widely referred to as a 'burqa ban", the wording of the law was left deliberately religiously neutral.
The company noted in the post that "life isn't easy" and went on to say they had received a fine for the commercial display outside the new shop.
His costume reportedly came to the attention of police after a member of the public reported him for breaking the law.
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.
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The law - which prevents people from concealing their face - applies to all public places, including transport facilities, and police have the power to demand the removal of concealing veils.
As well as burkas, the law also bans clown disguises, medical masks outside of a hospital context, or scarves that cover the face.
Austria's new burqa ban became a cynosure once again and this for a freaky reason when a man dressed as a massive shark was arrested.
Police have called for the new law to be clarified although it is believed Halloween events will not be affected by the legislation, adds the paper.
The measures were seen as an attempt to counter the rise of the far-right Freedom Party, which nearly won the presidency in December 2016.
An Algerian billionaire wearing a Halloween mask has led a protest outside the Austrian interior ministry in Vienna, promising to pay the fines of any women who are prosecuted for wearing the niqab or burka.