The statue sculpted in tribute to author Hans Christian Andersen draws about 1 million visitors a year and is targeted occasionally by vandals. On Tuesday, the statue's face, left arm and lap were found doused with red paint.
In 2004, someone put a burqa, the head-to-toe Islamic robe, on the statue, along with a sign questioning Turkey's bid to join the European Union.
The bronze statue by Edvard Eriksen has sat on a rock in Copenhagen harbor since 1913.