The incident took place on Friday morning in Manhattan, affecting the doors and a section of the facade of the Polish Consulate General, as well as the nearby "Karski Bench" on the corner of 37th Street and Madison Avenue.
Consul General Mateusz Sakowicz described the act as "unambiguous vandalism that must be condemned".
He said authorities were treating the matter as a security priority and were working alongside consular staff on the investigation.
Sakowicz said there was no reason to suspect a political motive.
"It simply looks like an act of vandalism. What the motives were, I cannot say," he told the PAP news agency.
Staff removed paint where possible, with city services expected to handle the remainder using specialist chemicals.
The bronze sculpture, unveiled in 2000, has been targeted before – most recently in 2017.
Jan Karski was a courier for the Polish Underground State who smuggled reports of the Holocaust to the Allies during the Second World War.
After the war, he became a professor at Georgetown University and one of the most prominent historical witnesses of the 20th century.
(ał)
Source: PAP, tvn24.pl