In a video capturing the incident, a white man in a short sleeve shirt and shorts pulls a paint can out of a paper bag and tosses red paint across the huge, yellow letters of the mural.
Police said the vandal fled down 56th Street after tossing the paint. The person has not been caught.
Authorities are asking individuals with information regarding the vandal to come forward.
The city plans to repair the mural. It is one of five Black Lives Matter murals announced last month by the city meant to honour civil rights activists.
President Donald Trump opposed the mural, claiming it would “further antagonise New York’s finest” and called it a “symbol of hate”. He also suggested the mural was “denigrating this luxury Avenue”. referencing the luxury shopping outlets along Fifth Avenue.
Just before the mural was painted, Mr Trump wrote a tweet subtly suggesting the NYPD should not allow the city to complete the project.
“Maybe our GREAT Police, who have been neutralized and scorned by a mayor who hates & disrespects them, won’t let this symbol of hate be affixed to New York’s greatest street,” Mr Trump tweeted.
Earlier this month, Mr Trump signed an executive order protecting monuments and statues from vandals, with a maximum 10 year prison sentence attached. The order was a reaction to weeks of protesters toppling and defacing statues, particularly those of Confederate generals.
A couple that defaced a Black Lives Matter mural in California were charged with a hate crime.