The arrested individuals were on their way to or at Fælledparken in Copenhagen, where International Workers' Day demonstrations and speeches traditionally take place.
Four people were arrested early in the afternoon: three for breaking regulations over the wearing of masks and one for violence against a police officer.
“After the arrests… they quickly calmed down,” Deputy Inspector Allan Wadsworth-Hansen of Copenhagen Police said.
“However, there were some smoke bombs thrown at the time of arrest,” Wadsworth-Hansen added, while stressing that the Fælledparken event itself had proceeded peacefully.
Four further arrests were made later in the day: one at the Israels Plads square and three at Fælledparken.
The later arrests were made variously for a law and order offence, possession of a knife, attempted violence and breaking mask regulations.
An attempted confrontation between a far-left and far-right group occurred in the late afternoon, Wadsworth-Hansen also said.
“We went between the two groups and kept them separated, so no confrontation resulted,” the officer said.