Key arguments from proponents of the new law centered on an alleged need to ensure that no Muslim women or girls are being forced to wear full-faced clothing, maintaining that this ban would help ensure better integration of asylum-seekers and migrants into Danish society.
Others wore the body-length burqa, which covers the eyes with a mesh screen.
The ban also targets other accessories that hide the face such as balaclavas and false beards.
Demonstrators, often with children in tow, chanted "no racists in our streets" and "my life, my choice" during the three-hour rally.
A spokesman for the Copenhagen police said they did not plan to fine the protesters who violated the ban.
One protester, Sabina, 21, a student teacher who declined to give her last name because other members of Women in Dialogue have received threats, called the law oppressive and Islamophobic.
It is estimated that Muslims account for about 7 percent out of the total population of 5.6 million in Denmark.
Women found violating the ban may be instructed by police to remove their veils, ordered to leave public areas, or can face fines of up to about $1,600 Dollars or six months in jail. Women who have never caused any problems for Denmark, women who work, study and are contributing members of society.More news: Drake drops In My Feelings video chock full of cameos
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A 30-year-old Muslim woman interviewed ahead of the protests in the daily Berlingske, identified only as Sarah, said she had "lost faith in the system".
Born and raised in Denmark by parents who emigrated from Turkey, she has worn the niqab since she was 18. "I'm for the right of the people to wear whatever they want whether they be a Muslim or a punk".
"I will hope that we can change the climate or the narration of what a Muslim woman is and maybe they will change the law or subtract it someday", she added. "So much of politics is hypocritical".
Also on Wednesday, dozens of supporters of the ban gathered to celebrate its coming into effect, saying that the face veil deprived women of their freedom, DR reported.
Only about 150 women are estimated to wear the face veil in Denmark.
'If the intention of this law was to protect women's rights it fails abjectly.
This morning, Amnesty International's Deputy Europe Director Fotis Filippou said all women "should be free to dress as they please and to wear clothing that expresses their identity or beliefs".
In May, the Danish parliament banned the wearing of face veils in public, joining France and some other European countries to uphold what some politicians say are secular and democratic values.