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.
The Anti-Mask Act, prohibiting full-face coverings including headwear worn by some Muslims, came into force on 1 October.
The law states faces must be visible from the hairline to the chin in public places.
Off-piste ski masks, surgical masks outside of hospitals and party masks are included.
But the law, which is popularly known as the “burka ban”, is mostly seen as aimed at the conservative Islamic clothing.
Those who break the law can be fined €150 and police are allowed to use force to make people show their faces.
The man arrested was apparently dancing outside the store at the time police arrived, according to Heute newspaper.
He is understood to have refused several requests to take off his shark’s head.
Heute said he told police he was only doing his job.
The managing director of the advertising agency responsible for the campaign, Eugen Prosquill, told the newspaper he was not aware the new law applied to mascots.
“It would be a pity if there were no mascots left,” he said.
Austria’s “burka ban” came after similar restrictions were brought in across France and Belgium and partial bans introduced in the Netherlands, Italy and Spain.