Denmark woke up on Friday to the words "racist fish" scrawled across the base of the "Little Mermaid", the bronze statue honouring Hans Christian Andersen’s famous fairy tale that perches on a rock in the sea off a pier in Copenhagen.
Police said it had not yet identified the perpetrators.
The 107-year-old sculpture, which is visited by one million tourists each year, has been vandalised before, including by anti-whaling campaigners and pro-democracy activists, twice suffering decapitation.
"We consider it vandalism and have started an investigation," a spokesman for the Copenhagen police said.
Protesters of the Black Lives Matter movement around the world have in recent months rallied against statues of historical figures who played a role in racist oppression, such as slave traders and colonialists.
The Little Mermaid has not been part of this debate but last year a Disney live-action remake of the 1989 animated film of the same name was the subject of controversy after African American actress Halle Bailey was cast in the central role.
"I am having a hard time seeing what is particularly racist in the fairy tale "The Little Mermaid," Ane Grum-Schwensen, a researcher at the H.C. Andersen Center at the University of Southern Denmark, told local news wire Ritzau.