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.
Both women were charged with disturbing the peace.
The episode took place in the center of Hørsholm center where the woman with niqab came up to top with another woman by an escalator in the center.
The new law bans wearing a burqa, which covers a person's entire face, or the niqab, which only shows the eyes, in public.
Danish police have fined a woman for wearing a niqab in a shopping complex, local media reported.
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Stambul, who is not aboard, said that about 40 activists from 15 countries, including two from France, were taking part. Israel says that Hamas, the militant group that rules Gaza, is using the protests as a cover for cross-border attacks.
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On Wednesday night protesters gathered in the capital to demonstrate against law, with women in traditional burqas and veils standing alongside people with makeshift coverings.
"Whilst some specific restrictions on the wearing of full face veils for the purposes of public safety may be legitimate, this blanket ban is neither necessary nor proportionate and violates women's rights to freedom of expression and religion", said Fotis Filippou, Amnesty's deputy Europe director.
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.
"All women should be free to dress as they please and to wear clothing that expresses their identity or beliefs". 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. France became the first European country to ban the full-face veil from public spaces in 2011, with fines of up to €150 (Dhs640) for those caught wearing the garment.