It becomes the latest in a number of EU countries to pass such a ban, which mainly affects Muslim women wearing a niqab or burka.
The law was passed by 75 votes to 30 in parliament on Thursday and will come into force on 1 August.
Those violating the ban will be forced to pay 1,000 kroner (£118; $157), with fines ten times higher for repeat offenders.
The wording of the new legislation does not specifically mention Muslim women but says that "anyone who wears a garment that hides the face in public will be punished with a fine".
Speaking about the law, Denmark's Justice Minister Søren Pape Poulsen said: "In terms of value, I see a discussion of what kind of society we should have with the roots and culture we have, that we don't cover our face and eyes, we must be able to see each other and we must also be able to see each other's facial expressions, it's a value in Denmark."
Amnesty International has described the Danish vote as a "discriminatory violation of women's rights".
But the European Court of Human Rights last year upheld a Belgian ban on full-face veils, saying that communal harmony trumped the individual's right to religious expression.
Where else in Europe has similar laws?
France was the first European country to ban the full-face veil in public places in April 2011, seven years after it introduced a law prohibiting conspicuous religious symbols in state schools.
It was followed a few months later by Belgium, which outlawed any clothing that obscures a person's identity in a public place.
Full or partial bans have since been passed in Austria, Bulgaria and the southern German state of Bavaria, with the Dutch parliament agreeing a ban in late 2016, pending approval from the country's higher chamber.
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A protest in Montreal in 2013 against a proposal to outlaw public sector employees from wearing face veils. Quebec enacted a face veil ban on Wednesday
That means it is illegal for them to ride a public bus, work as a doctor or teacher, or receive publicly funded health care while covering their faces.
The government said people could apply for exemptions, but some are already built into the law: Doctors are allowed to wear a surgical mask that covers the lower half of the face, but not a veil that does the same thing.
Quebec’s minister of justice, Stéphanie Vallée, said the law fostered social cohesion, but critics disagreed. Ihsaan Gardee, the executive director of the National Council of Canadian Muslims, called it “an unnecessary law with a made-up solution to an invented problem.”
The French-Algerian businessman Rachid Nekkaz at a protest in Vienna. He said he would pay the fines of women punished for wearing full-face veils in Austria.
Austria’s ban on face coverings took effect in October. The law forbids women from wearing garments like burqas or niqabs in public, including in universities, public transportation or courthouses. Violators can be fined 150 euros, or about $175.
Muna Duzdar, a state secretary in the office of Chancellor Christian Kern, told reporters in May that the measure was part of a broader package intended to help immigrants assimilate to life in Austria.
But the law has proved difficult to enforce.
Last week, the police issued citations to two people: a male activist protesting the law by wearing a mask and a suit covered in €100 notes; and a man wearing a shark costume as part of a sidewalk advertising campaign for a chain of computer stores called McShark, who refused to remove the head piece when asked to do so.
France has long been riven by tensions between its Muslim population, Europe’s largest, and those who support the state ideology of secularism.
In 2011, France became the first country in Western Europe to ban face-covering garments like the burqa or niqab in public, although the law did not explicitly mention Islam. The move made it illegal to cover one’s face in public places including streets and stores, as a security measure. Those who break the law face fines of up to €150.
The law has been divisive in France, which has long been riven by tensions between its Muslim population, Europe’s largest, and those who support the state ideology of secularism.
Last year a string of beach towns went one step further, driven in part by a string of deadly terrorist attacks, and banned the burkini, a full-body swimsuit worn by some Muslim women.
A woman wearing a niqab in Brussels in 2010.
A law that banned face-covering garments in public also came into effect in Belgium in 2011. Violators could be sentenced to seven days in prison and face a fine of €137.50.
The law was quickly challenged in court by two Muslim women who said it violated their right to privacy and freedom of religion.
But in July, the European Court of Human Rights ruled against them. It said it agreed with Belgium’s argument that the law was meant to “guarantee the conditions of ‘living together’ and the ‘protection of the rights and freedoms of others.’”
Midday prayers at a mosque in Berlin.Credit
A law banning face coverings while driving took effect in Germany this month, coming on the heels of legislation prohibiting anyone in the civil service, military or working for an election from covering their faces.
Bavaria took the measure one step further, banning teachers and university professors from covering their faces.
Chancellor Angela Merkel has faced increasing pressure from the right in recent years and supported the new legislation last year as part of measures to help assimilation into society. She told reporters at the time, “From my standpoint, a fully veiled woman scarcely has a chance at full integration in Germany.”
There are roughly four million Muslims in Germany, about a quarter of whom arrived from 2015 to 2016 from Syria, Afghanistan and Iraq, after Ms. Merkel opened the border.
Muslims in Ribnovo, Bulgaria, in 2014. The country passed a law on face coverings in 2016.
Following in the footsteps of its larger European Union partners, Bulgaria banned face-covering garments in government offices, schools and cultural institutions in 2016.
Lawmakers who supported the measure denied it was discriminatory. They said it was intended to help the country respond to potential security issues posed by the migrant crisis.
But most Muslims in Bulgaria are native-born members of the country’s long-established Turkish minority. They make up about 12 percent of the population and few of them wear niqabs or other face coverings, according to Reuters.
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