Michael Hoejer, deputy national police commissioner, said: "The bad [news] is that there's been a lot of vandalism; they've set fire to cars, garbage containers and in some cases buildings.
"The good news is that we've made a lot of arrests."
The spate of vandalism started last weekend and is believed to have intensified after Danish newspapers reproduced a cartoon of Muslims' Prophet Muhammad on Wednesday.
The decision, seen as a gesture of media solidarity after police revealed an alleged plot to kill the cartoonist, also sparked protests in Pakistan and Bangladesh.
Jan Marker, a spokesman for the Danish police, said: "Many people also think it's because the youths are bored.
"We are in the process of putting a profile of these youngsters together to see if we can come up with what is driving them ... But the only thing we know for sure right now is that most of them are under 18."
Across the country more than 30 cars and 50 containers have been torched, and buildings such as schools and garages have also been targeted.
While police have said they are not sure what has triggered the violence, observers say immigrant youths are protesting against perceived police harassment.