While the wording of the new legislation does not specifically mention Muslim women-it cites "anyone who wears a garment that hides the face in public" as grounds for a penalty-the law has been widely dubbed a "burqa ban".
Justice Minister Soren Pape Poulsen has said that officers would in practice fine them and tell them "to go home".
People will only be allowed to cover their faces for a "recognisable purpose" when the law comes into force.
Those ignoring the law could face an initial fine of £118 - followed by up to six months in jail or an £11,000 fine for repeat offences. 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, Belgium, Bulgaria and France all have laws in place to prevent wearing the religious garment in public.
The justice ministry and the police now will write more detailed guidelines. The spokesperson on immigration and integration of the Danish People's Party explicitly cited a decade of efforts to ban the burqa and niqab in public, and vowed to push for new measures against the "Islamicisation of Denmark". The study said that of the 150 women who wear the Islamic face veil in Denmark, around half are ethnic Danes who converted to Islam.
"Many people believe that men force us to wear the niqab or burqa".
Van Gulik added that the law fails "abjectly" if its goal is to protect women's rights.
Over the last decade or so, there has been a growing movement to ban full-face veils in countries in Europe. "Instead, the law criminalises women for their choice of clothing and in so doing flies in the face of those freedoms Denmark purports to uphold". Syria too has a ban on the use of face veils since 2010.
Most notably, in 2011, French President Francois Fillon in a decree banned the full-face veils from public spaces.