The iconic landmark, which sits at the entrance to Copenhagen harbour, has been targeted by vandals on numerous occasions over the years.
They have previously dislodged the 107-year-old off her stone perch, painted her and even beheaded her.
The city’s police said no one had claimed responsibility for the latest assault.
“We consider it vandalism and have started an investigation,” a spokesman said.
The bronze statue was created as a tribute to the Hans Christian Andersen fairytale about a sea king’s mermaid daughter who longs to become human and falls in love with a prince.
The case comes as monuments around the world are being reconsidered in light of anti-racism demonstrations.
However, Ane Grum-Schwensen, a researcher at the HC Andersen Centre at the University of Southern Denmark, told the Danish news agency Ritzau: “I am having a hard time seeing what is particularly racist in the fairytale The Little Mermaid.”
Some Twitter users created the hashtag #NotMyAriel to claim that the main role should be played by a white star.
But Bailey offered a graceful reaction to the backlash, saying: “I don't pay attention to the negativity. I just feel like this role was something bigger than me, and greater.”