Danish nationals have been urged to leave Indonesia over fears they may be targeted in the row over cartoons satirising the Prophet Muhammad.
Danish embassies have been the target of angry protestors
The foreign ministry says intelligence reports suggest an extremist group is actively seeking out Danes and Danish interests in Indonesia.
It is the most serious yet in a string of advisories issued by Copenhagen to Danish nationals in Muslim countries.
Denmark has temporarily shut its missions in Indonesia, Iran and Syria.
Embassy staff in the first two countries were withdrawn after threats were made against them, the Danish Foreign Ministry said in a statement.
Diplomatic staff were pulled out of Damascus because "Syrian authorities reduced their protection to an unacceptably low level", it said in an earlier statement.
As yet, no Danes have suffered injury despite the violence of some of the demonstrations that have swept across the Muslim world.
The BBC's Julian Isherwood in Copenhagen says the intelligence reports are of such a concern to the foreign ministry, they are taking no chances.
"Concrete information indicates than an extremist group wishes to actively seek out Danes in protest for the publication of the Prophet Muhammad cartoons," the ministry statement read, without naming the group.