Violating the regulation results in a fine of 1,000 kroner ($156).
It has been reported that police were called to a shopping centre in Horsholm on Friday to confront a woman wearing a niqab garment covering her face. They're investigating CCTV footage to see if the other woman had deliberately tried to rip off the niqab.
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.
The legislation came into effect on 1 August.
According to a Reuters report, thousands of woman joined the protest and marched through the capital Copenhagen wearing veils after the law, which many feel violates freedom of religion and expression, was passed. The police told the ppaer that nothing indicates that the turmoil arose from the fact that one woman was wearing niqab.
Repeat offenders of the ban could be fined up to 10,000 kroner (£930).
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Chief of Police at North Zealand Police, David Borchersen, tells Politiken that the presence of police in Hørsholm Midtpunkt relates exclusively to the tumult between the two women, and nothing has to do with the fact that one with his attire contravened the law.
The new law bans wearing a burqa, which covers a person's entire face, or the niqab, which only shows the eyes, in public.
Protests in Denmark broke out over the new law, which also bans balaclavas, masks, and false beards.
"This ban will have a particularly negative impact on Muslim women who choose to wear the niqab or burqa".
The Danish parliament enacted the face ban in May, joining France and some other European countries to uphold what some politicians say are secular and democratic values.