Police were called to a shopping center in Horsholm, north of Copenhagen, where the woman had become involved in an altercation with another woman, police duty officer David Borchersen told the Ritzau news agency.
The woman was informed she would receive a fine of 1,000 kroner (RM632) in the post, and was told to either remove her veil or leave the public space.
Mr Borcher said: 'During the fight her niqab came off, but by the time we arrived she had put it back on again'.
Muslim and non-Muslim women protested in full niqab and balaclavas against the new law, which has drawn criticism for a number of human rights groups.
The two women were both charged with breaching the peace.
Since August 1, the country's much-debated "Burqa Ban" has prohibited full-body burqas, as well the niqab - Muslim dress which only shows the eyes.
It does not mention burkas and niqabs by name, but warns that anyone who wears a garment that hides their face in public will be fined.
Past year the European Court of Human Rights upheld a similar Belgian ban, saying that communal harmony trumped an individual's right to religious expression.
People demonstrate in Copenhagen, Denmark supporting the new ban on garments covering the face.
Fines can go up to $1,552 for repeated violations.
People are allowed to cover their face when there is a "recognisable purpose" such as protection from cold weather, or cycling helmets.
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.
Belgium, France, Germany and Austria have already imposed bans or partial bans.