The Little Mermaid statue in Copenhagen, the city's most famous monument, has been vandalised but police and commentators were puzzled as to who might have done it and what their message really is.

"We can confirm that The Little Mermaid has been vandalised some time before 9am this morning," Copenhagen police said in a statement.

"An unknown person has written the words 'Racist Fish' on it. We are investigating the case."

The Little Mermaid, inspired by a character in Danish poet and author Hans Christian Andersen's 1837 fairytale of the same name, is a 175kg statue by sculptor Edvard Eriksen.

The statue has been vandalised numerous times over the years, including when the mermaid's head was stolen in 1964 and 1998, as well as when an arm was cut off in 1984. 

Often the vandalism is tied to a political message and in January someone painted "Free Hong Kong" on the same rock.

The meaning of the apparent racist accusation has however, so far, left some scratching their heads.

"Of course in general with literary works, you can read them with various glasses," Ane Grum-Schwensen, an expert employed by the HC Andersen Centre at the University of Southern Denmark, told broadcaster TV2.

"However, I do find it a little difficult to see, what would be especially racist in the adventure The Little Mermaid," she added.

According to police other statues around Copenhagen have also been vandalised with "various phrases". One of missionary Hans Egede, who launched Lutheran mission efforts to Greenland, and one of Mahatma Gandhi in the northwestern part of the city.

Police also said that on 16 June, someone had written "racist" on a statue of Danish King Christian IV, who ruled between 1588 and 1648.

Statues of historical figures in many countries have come under fire from activists protesting racism following the 25 May death of George Floyd, an African-American killed by a white police officer in Minneapolis in the US.