Police fought the street battles with hundreds of youths last week after squatters were evicted from the building in the blue-collar, multi-ethnic neighbourhood of Norrebro.
''We hope they will show their frustration only vocally, but we are out there on the streets, taking no chances,'' said Per Larsen, a Copenhagen police spokesman, in an interview on Danish television TV2 News.
A crane began tearing down the structure, which has been sealed off since the disturbances. The identity of the demolition company had been painted over on the crane and workers wore masks to conceal their faces.
Youths milled around and watched the work from outside the police cordon. Some were crying in the arms of their friends.
Demolition stopped before noon to investigate a possible asbestos problem, Danish media reported.
Tensions in the Danish capital subsided over the weekend after more than 600 arrests that included dozens of foreigners.
The conflict over the youth centre has simmered since 2000, when local government, which had lent the building to the youngsters since 1982, sold the site to a religious group.
Police evicted the squatters last Thursday, implementing a court order issued last year.
The religious group said today they did not yet have plans for the area after the demolition.
REUTERS PDM PM1707