Black paint was thrown on the bust of Mr Floyd and the name of the right-wing Patriot Front extremists was daubed on it.
The vandalism came just days after the statue was unveiled in the city.
Mr Floyd, 46, was murdered in May 2020 by Minneapolis police officer Derek Chauvin, who will be sentenced to prison for the killing on Friday.
His killing came after police officers responded to a call that he had used a counterfeit $20 bill at a convenience store in the city.
The murder was captured by bystanders on their phones and the viral video led to months of racial injustice protests across the United States.
New York Police Department officers discovered the damage in the early hours of Thursday.
“There are no arrests and the investigation is ongoing,” said an NYPD the spokesperson in a statement.
Mayor Bill de Blasio took to Twitter to condemn the act.
“Last night a far-right extremist group vandalized a statue of George Floyd in Brooklyn,” he tweeted.
“A racist, loathsome, despicable act of hate. The City Cleanup Corps is repairing the statue right now and a hate crime investigation is underway. We will bring these cowards to justice.”
It is believed the vandalism took place in a two hour window when NYPD officers were not located near the statue.
“You’re cowards. You did this at night when no one could see you. I’m restoring it in the day when everybody can see your hate,” she told the vandals.
The statue was created by artist Chris Carnabuci,
Mr Floyd’s brother, Terrence Floyd, said in a statement that the vandalism was “a perfect example of why we are so diligent in promoting change. As a community we should stand together in peace and in turmoil.”