The mutation has already been detected in 12 people
Denmark announced special restrictions for more than 280,000 people in the country's northwest on Thursday after a mutated version of the new coronavirus linked to mink farms was found in humans.
Copenhagen warned that the mutation could threaten the effectiveness of any future vaccine.
"From tonight, citizens in seven areas of north Jutland are strongly encouraged to stay in their area to prevent the spread of infection," Prime Minister Mette Frederiksen told a news conference.
She said people were being ordered not to travel there, while bars and restaurants would also shut.
"We are asking you in north Jutland to do something completely extraordinary," Frederiksen said, talking of a "real closure" of the region.
"The eyes of the world are on us," she added.
The World Health Organization is looking at biosecurity around mink farms in countries across the world to prevent further "spillover events."
Maria van Kerkhove, the WHO's technical lead for Covid-19, told a briefing in Geneva yesterday that transmission of the virus between animals and humans was "a concern," but added:
"Mutations (in viruses) are normal. These type of changes in the virus are something we have been tracking since the beginning."
The risk was much lower in animals other than mink, a second WHO expert said.
Denmark, the world's largest exporter of mink fur, raised concerns on Wednesday by announcing the slaughter of all mink in the country -- numbering 15 to 17 million spread over 1,080 farms -- following the discovery of the mutation which can be passed to humans.
The mutation has already been detected in 12 people -- 11 cases in the region being closed down, and one in another.
Scientists say virus mutations are common and often harmless.
Some experts have nevertheless called on Denmark to release more scientific data to better evaluate this one.
According to Danish authorities, this virus mutation doesn't cause a more severe illness in humans.
But it is not inhibited by antibodies to the same degree as the normal virus, which they fear could threaten the efficacy of coronavirus vaccines that are being developed around the world.
In north Jutland, health authorities believe around 5% of coronavirus patients could be carrying this mutated strain, but no recent case has been reported.
As such, Viggo Andreasen, epidemiology professor at Roskilde University, said the mutation had "quite a good chance" of disappearing, as long as it is effectively contained.
Denmark, a 5.8-million-strong country, has been relatively spared from the ravages of Covid-19 with 733 deaths reported.
But it imposed new national restrictions in October to curb a rapid spike in cases.