07 August, 2018
"During the fight her niqab came off, but by the time we arrived she had put it back on again", Borchersen said.
The woman was told she'd get a fine of 1,000 Danish kroner or about $155 and was told to take off the veil or leave the public.
Veiled women take part in a demonstration against the veil ban.
The other woman was also charged with disturbing the peace.
The controversial ban was met with resistance when it came into effect on Wednesday this week.
She had got into a fight with another woman, who had allegedly tried to rip off her veil in a shopping centre in Horsholm, which is around 15 miles north of Copenhagen. She was asked to remove the niqab or leave the public place.
Some Muslim women have said they will not adhere to the law - which carries a 10,000 ($1,500; £1,200) kroner penalty for repeat offenders.
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Coming into force on August 1, Denmark's ban prohibits the wearing of facial coverings such a balaclavas, masks and false beards.
Police took a photograph of the woman wearing the veil, before obtaining security camera footage of the incident from the shopping centre.
Both women have been charged for fighting in public, but the Muslim woman was also fined for failing to obey the new law.
Human rights campaigners have slammed the ban as a violation of women's rights, while supporters argue it enables better integration of Muslim immigrants into Danish society.
Hundreds of demonstrators gathered in Copenhagen wearing burqas and other face veils as the law went into effect Wednesday.
Denmark has become the fifth European country to enforce a law on full-face garments.
"All women should be free to dress as they please and to wear clothing that expresses their identity or beliefs".