The police took a photo of the woman in the niqab, as well as securing other video evidence from surveillance cameras in the shopping centre.
Police were called to a shopping center in Horsholm, north of Copenhagen, where the woman had become involved in an altercation with another woman, police duty officer David Borchersen told the Ritzau news agency.
She was given a 1,000 kroner fine (£120) after refusing to remove it on the request of the police.
A 28-year-old female was fined after getting into a fight with another woman, who had tried to tear of her veil.
Police are going through surveillance video to determine if the other woman deliberately ripped off the niqab.
The new law has provoked protests and criticism from human rights groups.
Ivanka Trump says she was 'vehemently' opposed to separation of families
Hill also empathized with Ivanka , claiming "she's been on the receiving end of numerous unfair smear attacks the media have waged against her family".
Toby Alderweireld Set To Sign For Manchester United 'In Next 48 Hours'
The new season is approaching with the transfer window set to slam shut next Thursday. What's more, it's claimed the deal will be made official within the next 48 hours.
Ton a test of physical, mental strength: Kohli
Cricket is such a game that you can chase down small totals easily with one big partnership. The 20-year-old left-armer proved he can be a major weapon if the ball is swinging.
They said both women were charged with violating the peace and said one had also been charged with violating the full-face veil law.
Though the law states that "anyone who wears a garment that hides the face in public will be punished with a fine" and does not explicitly mention the traditional piece of clothing worn by Muslim women, according to a New York Times report, many protestors claim that the ban particularly targets minorities.
Denmark's facial covering law came into effect on Wednesday, and brings the country in line with similar prohibitions in France and Belgium.
The Danish law allows people to cover their face when there is a "recognisable purpose" like cold weather or complying with other legal requirements, such as using motorcycle helmets.
Human rights campaigners have slammed the ban for violation of women's rights, while supporters argue the ban enables better integration of Muslim immigrants into Danish society.