Images of the tourist attraction show the red, blue and white stripes which form the Russian flag painted onto the rock on which the Mermaid sits.
Police said on Thursday morning that they had sent a patrol out to the statue.
“We will naturally initiate an investigation to find out who did this and how and when it happened,” duty officer Martin Kajberg of Copenhagen Police said.
The famous statue has been vandalised several times during its 110-year history, often with political motives but sometimes for other reasons.
The last few years alone have seen it painted blue, painted red, and tagged with a message of support for Hong Kong democracy activists.
Going further back, the mermaid’s head was stolen in 1964 and 1998 and her arm was cut off in 1984. In 2003, it was stolen from its plinth before being recovered and restored.
It has also been dressed in a burka as well as Swedish and Norwegian football jerseys.
The Little Mermaid is located on the Langelinie promenade on the northern side of Copenhagen Harbour.
The statue, made by sculptor Edvard Eriksen in 1913, depicts the character from Danish author Hans Christian Andersen’s fairy tale.