The 107-year-old bronze statue, which pays tribute to the 1837 fairytale by Hans Christian Anderson, is sat on a rock in the water off a pier.
Police in Copenhagen said they have not yet identified the perpetrators, but confirmed they are now investigating the incident.
A spokesman said: "We consider it vandalism and have started an investigation."
The statue - which is visited by millions of tourists each year - has been vandalised before, having even been decapitated twice in the past.
Groups behind previous incidents have included anti-whaling campaigners and pro-democracy activists.
While many statues have been reconsidered in the wake of the Black Lives Matter movement, Copenhagen's Little Mermaid piece has not yet been a part of this debate.
The fairytale's Disney live action remake of the 1989 animated film became the subject of controversy last year after African American actor Halle Bailey was cast in the lead role.
Ane Grum-Schwensen, researcher at the H.C. Andersen Center at University of Southern Denmark, told local news wire Ritzau: "I am having a hard time seeing what is particularly racist in the fairy tale 'The Little Mermaid'.
After a statue of slave trader Edward Colston was thrown into the Bristol harbour by Black Lives Matter demonstrators recently, the city's mayor said a commission of 'historians and city placemakers' would be launched dedicated to 'researching and sharing Bristol's rich and varied areas and stories'.
Mayor Marvin Rees said: "The events over the last few days have really highlighted that as a city we all have very different understandings of our past.
"The only way we can work together on our future is by learning the truth of our beginnings, embracing the facts, and sharing those stories with others. This is why this commission is so important.
"Bristol's journey to become the modern city it is today includes a history of huge disparities of class, race and gender and the struggles for equality.
"Our history includes the growth of education, the struggles of workers for pay and working conditions, and Chartists and suffragettes campaigning for emancipation.
"Our story includes the impacts that wars, protests, slavery and freedom have had on our citizens. Crucial to our heritage has been the harbour and the docks, manufacturing and industry, research and innovation, transport, slum clearances, housing, modern gentrification and faith.
"Education of our history has often been flawed. More accuracy of our city's history which is accessible to all will help us understand each other, our differences, our contradictions and our complexities."