"It is incompatible with the values in Danish society and disrespectful to the community to keep one's face hidden when meeting each other in public spaces," Justice Minister Søren Pape Poulsen said in a statement.
"With a ban on covering the face, we are drawing a line in the sand and underlining that in Denmark we show each other trust and respect by meeting face to face," he added.
The niqab is a full veil with a small slit for the eyes, while the burqa is a full veil that covers the head and body with a mesh screen over the eyes.
The proposal is to be assessed by non-governmental human rights organisations and possibly re-written to take their remarks into consideration.
The centre-right government is expected to present a bill to parliament in the spring.
With the support of the country's second largest party, the anti-immigration Danish People's Party, the proposed legislation is likely to be adopted.
A violation of the ban would lead to a fine of 1,000 kroner (134 euros).
Repeated violations would be fined up to 10,000 kroner.
The proposed ban says the "burqa, niqab and balaclavas where only eyes and mouth are visible are examples of clothes that hide the face".
But covering the face in a recognisable manner, such as wearing winter clothing, sports gear and masks for festivities, are exempted, in an apparent change from a draft version of the proposal reported last month.
The actual number of people who wear either the burqa or niqab in Denmark is not known precisely.
The most recent figures come from 2010, when a government report estimated the number to be between 150 and 200 women, with the majority of these wearing the niqab, rather than the burqa.
"I don't think there are many who wear the burqa here in Denmark. But if you do, you should be punished with a fine," Poulsen told reporters, according to news agency Ritzau.
The full-face veil is a hot-button issue across Europe.
The European Court of Human Rights last year upheld a Belgian ban on wearing it in public.
France was the first European country to ban the niqab in public places with a law that took effect in 2011.
Spain's highest court annulled in 2013 a ban on the full-face veil in public buildings that had been brought in three years earlier by the northeastern region of Catalonia.