The mass cull was ordered after it was discovered that a mutated version of the coronavirus found among minks in Danish farms can be transmitted to people, though there is no evidence so far that it is more risky or resistant to vaccines.
Testing of the mink herd in Ireland detected no positive results to Covid-19 to date.
Similar concerns have prompted Ireland's Chief Medical Officer to call for the culling of the Irish farmed mink population as they represent an "ongoing risk to public health".
"The government has been promising for a long time now to shut these fur farms, after the Solidarity - People Before Profit Bill introduced previous year", Deputy Murphy said.
Denmark's Agriculture Minister Mogens Jensen announced Wednesday he was stepping down due to mishandling a cull of the Danish mink population.
"Mink farmers continue to operate in full compliance with all legislative and animal welfare requirements and have co-operated fully with these efforts".
Last week it emerged that Denmark's government did not have the legislation in place for such a directive, though a deal was later reached to create a retroactive legal basis for the cull.
This comes after a mutated strain of the virus was found on a mink farm in Denmark. "Mainly because of the number of mink infected with COVID-19".
Now the Department of Agriculture has informed the owners of three mink farms in Ireland that their mink are to be culled to halt the potential spread of a mutated form of the Covid-19.
The Department added that no mink have been imported into Ireland during 2020. The Covid-19 variant could be passed to humans and could derail vaccination plans were it to spread internationally.
Poland is one of the world's top producers of mink fur, with 354 farms, containing around 6 million minks. The "mink coronavirus" has proved to reduce antibody efficacy and has been identified in more than 300 variants, according to research from University College London (UCL) Genetics Institute as cited by the Guardian. It said all farms would be permitted to "harvest" fur from the animals when they are culled in coming weeks.
Dr. Hans Kluge, the World Health Organization's regional director for Europe, described mink farms on Thursday as "a reservoir where the coronavirus is thriving".