A smaller demonstration arranged by "For Frihed" (For Freedom), which is pro face veil ban, also took place.
The government said it is not aimed at any religion and does not ban headscarves, turbans or the traditional Jewish skull cap.
A spokesperson for group Kvinder I Dialog (Women In Dialogue) told the Independent: "The goal of this demonstration is to show that we do not accept this kind of unjust treatment regardless of who we are dealing with". Now that these women face penalties for covering their faces in public, Sabina says they will have to do the majority of their work on social media from their homes.
Violators will be punished with a fine of up to 1,000 kroner ($156).
Even so, protestors cited the right for women to dress as they wish and said the law unfairly targets Muslim women, who make up 5 per cent of the country's population.
"Everybody wants to define what Danish values are", said Meryem, 20, who was born in Denmark to Turkish parents and has been wearing the niqab since before meeting her husband, who supports her right to wear it but feels life could be easier without.
Women in Dialogue, which was created in response to the ban's initial proposal past year, did a lot of its work on the streets or at universities, with veiled women handing out fliers and giving speeches to promote dialogue and educate people about the niqab.
'We need to send a signal to the government that we will not bow to discrimination, ' student Sabina, 21, told Reuters.
In May, Denmark became the latest in a series of European nations to ban face veils in public, saying that it is a necessary measure to uphold the country's secular values.
First-time offenders risk a fine of 1,000 kroner (£120).
"Its aim is to isolate a small religious group from society", Youssef said, adding that only 50 women wore veils in Denmark.
Belgium, France, Germany and Austria have already imposed bans or partial bans.
Hundreds of people have gathered on the streets on Copenhagen to protest against a new ban on face veils being worn in public.
The protesters, many wearing a niqab or burqa, marched from the central, left-wing district of Norrebro to Bellahoj police station on the outskirts of the capital.
The law was approved in the Danish parliament in a 75-30 vote with 74 absentees.
Moreover, it allows people to cover their face when there is a "recognisable purpose" such as cold weather or complying with other legal requirements, for example using motorcycle helmets under Danish traffic rules. Instead, the law criminalises women for their choice of clothing - making a mockery of the freedoms Denmark purports to uphold'. In 2016, Denmark also adopted a law requiring newly arrived asylum-seekers to hand over valuables such jewelry and gold to help pay for their stays in the country.