First-time offenders risk a fine of 1000 kroner (US$156). Repeat offenses could trigger fines of up to 10,000 kroner or a jail sentence of up to six months.
Anyone forcing a person to wear garments covering the face by using force or threats can be fined or face up to two years in prison.
Austria, France and Belgium have similar laws.
The justice ministry and the police now will write more detailed guidelines. Those "should be very concrete" as to what will be banned, said Bjoern Elmquist, a lawyer who has been a prominent opponent of the law.
If it turns out to focus only on women in the niqab or burqa, it could amount to discrimination against a minority group and hence be against the law, Louise Holck of the Danish Institute for Human Rights told TV2 television.
- AP