"We have detained 23 people in the wake of the unrest that began yesterday and continued through the night. We plan to continue proceedings with regard to six of them today," the Copenhagen police wrote on Twitter.
In a Twitter message, Danish Prime Minister Lars Lokke Rasmussen has condemned the incident as a "senseless provocation."
On Sunday, the leader of the Stram Kurs party, Rasmus Paludan, and his supporters staged a demonstration in Norrebro, one of Copenhagen's districts, which is home to a significant Muslim community.
The unrest broke out when local residents attacked protesters. The police had to use tear gas.