Grey paint was thrown across the statue on Sunday, police said, just two days after it was set up in Union Square. Clean-up efforts by community volunteers are now underway.
In a BBC report the 6ft (2m) tall bust of Floyd was on display earlier in Brooklyn, where it was vandalised with black paint.
Security footage from around 10:00 local time shows a man holding a skateboard and mixing paint behind the sculpture before getting on his skateboard, splattering it across the face of the statue and riding away.
Floyd was murdered by a Minneapolis police officer in 2020.
His death incited a wave of global protests over racial justice.
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