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.
Violating the regulation results in a fine of 1,000 kroner ($156).
Danish news agency Ritzau reported that police were called to a shopping centre in Horsholm, a city of 46,000 close to Copenhagen, to confront a woman wearing a niqab garment covering her face.
Police spokesperson David Borchersen said a fight broke out after the Muslim woman walked into the other woman, who tried to rip her face veil off, at the top of some escalators.
Local media report a 28-year-old woman was fined after getting into a scuffle with a woman trying to remove her veil.
Both women have been charged for fighting in public, but the Muslim woman was also fined for failing to obey the new law.
As of August 1, wearing full-body burqas and the niqab, a veil worn by some Muslim woman that only shows the eyes, in public carries a fine in Denmark.
The ban also targets other accessories that hide the face such as balaclavas, masks and false beards.
The new burka law means that all forms of clothing that cover the face are now banned in public spaces, unless they serve a creditable goal.
People are allowed to cover their face when there is a "recognisable purpose" such as protection from cold weather, or cycling helmets.
Repeated offenders could be fined as much as 10,000 kroner (£1,193).
Supporters of the law, meanwhile, claim the law will better integrate Muslims into Danish society.
Belgium, France, Germany and Austria have already imposed bans or partial bans.