Anders Hansen, a spokesman for the local police, said vandals had pushed over headstones, smashing several into pieces, at the cemetery in Esbjerg.
Esbjerg is Denmark's fifth biggest city and is 250km west of the capital, Copenhagen.
"We don't know who did this," Hansen said, adding the attack probably happened late on Saturday or early on Sunday.
The cemetery has both Christian and Muslim graves, but only the Muslim graves were desecrated, he said.
The attack came at a sensitive time, with outrage sweeping the Muslim world over offensive cartoons published
in a Danish newspaper.
"I strongly condemn this disgraceful act and deeply regret that Muslim graves have been desecrated"
Anders Fogh Rasmussen,
Anders Fogh Rasmussen, the Danish prime minister, said in a statement: "I strongly condemn this disgraceful act and deeply regret that Muslim graves have been desecrated."
He said he denounced every act aimed at offending people because of their religious or ethnic background.
"Vandalism against cemeteries is a criminal act and authorities will take the necessary steps to find those responsible and bring them to justice," he said.