"I will comply with the law, as I've always done. I'm keeping my head high," Vammen said, adding that he would probably pick up mink farming again when the ban ends.
The bill was passed by 55 votes to 43 in parliament on Monday, with the main opposition parties, the central-right Liberals and the populist Danish People's Party, voting against the new law.
Many who voted for, like many of the country's officials fear that the mutated variant could cause long term issues with the effectiveness of future vaccines.
In late November, hundreds of mink culled and buried into the ground started to re-emerge from their graves because they were not buried deep enough.
"Danish mink farmers have sacrificed their life's work for the common good. We owe them a big thank you," Rasmus Prehn, the country's agriculture minister wrote on Twitter after the new law was announced.
The Nordic country is the world's biggest producer of mink fur.
But the decision now leaves the future of the industry in the country in doubt.