Between 200 and 250 people had gathered in Copenhagen and dozens in the city of Aalborg in Denmark's north, according to media reports citing police accounts.
Organised by a group calling itself “Men in Black”, the demonstrations targeted restrictions imposed to curb the spread of the coronavirus.
Protesters shouted: “Freedom for Denmark, we have had enough,” according to media reports.
In TV broadcasts and video posted to social media, police in riot gear could be seen clashing with protesters in Copenhagen, who lit fireworks and threw bottles.
Four people were arrested in the capital, two for violence against a police officer, one for violating the fireworks code and one for not following directions from a police officer.
Rasmus Schultz, coordinating officer with the Copenhagen police, told public broadcaster DR that some of the protesters were people that they recognised from the “hooligan environment”.
In Aalborg, five people were arrested, all for violating the fireworks code.
Responding to a surge in virus cases and the threat of recently discovered variant strains believed to spread faster, Denmark on Tuesday announced even tighter measures on top of a partial lockdown in place since mid-December.
In addition to existing measures like working from home and the closure of schools, bars, restaurants and most shops, gatherings of more than five people were banned — down from 10 — and people were asked to keep two metres (six feet) apart, rather than one metre.
On Friday, the country banned entry for foreigners without a negative virus test from the previous 24 hours.
It also advised against all travel abroad and announced that airlines flying to Denmark would need to make sure that all passengers had tested negative to be able to land.