Law enforcement officers arrived on call at a shopping centre North of Copenhagen, where there was a fight between two women.
The woman was told she would receive a fine of 1,000 kroner (Dh570) in the post, and was told to either remove her veil or leave the public space.
The woman came to police attention when a scuffle broke out between her and another woman at a shopping centre in the north-eastern region of Nordsjaelland.
When the ban went into effect, dozens of women came out in the Danish capital, Copenhagen, to protest it. She was asked to remove the niqab or leave the public place.
Clicked by Reuters photographer Andrew Kelly, the photo features a Danish policewoman embracing a visibly emotional woman protesting against the ban. The women pushed to each other and uprorious scenes arise in which the Niqab, among other things, is being torn by one woman.
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Police obtained CCTV footage of the incident. Following this new law, first-time offenders face a fine of 1,000 kroner (around $150) while repeated offenses could lead to fines of up to 10,000 kroner (around $1,500) including a jail sentence of up to six months. Other European countries have similar bans.
The ban also targets other accessories that hide the face such as balaclavas, masks and false beards.
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.
Both women have been charged for fighting in public, but the Muslim woman was also fined for failing to obey the new law.
"Denmark's ban is part of a worrisome trend that only marginalizes Muslim women in Europe and penalizes them for expressing their beliefs", Women's Rights Division researcher Hillary Margolis wrote.