The famous statue, which is one of the Danish capital's biggest tourist draws was found with the paint damage on Thursday.
No-one has taken responsibility for the act and it is not known when the vandalism took place.
Vandals painted the white, blue and red stripes of the Russian flag across the front of the stone.
The bronze statue was made 110-years-ago as a tribute to Danish author Andersen, who first published The Little Mermaid book in 1837.
Edvard Eriksen sculpted the stone which weighs 175kg (385lb) and stands 1.65 metres (5.4 foot) tall.
Vandals have long targeted the figure and have previously blown the mermaid off the rock on which it is perched, at the entrance of Copenhagen's harbour. It has also been beheaded and painted over before.
Denmark, which is a member of the North Atlantic Treaty Organisation (NATO), has condemned Russia's invasion of Ukraine since it began in February 2022.
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