The graffiti was found at Roberto Clemente Skate Park in Brentwood. The park opened in March following years of delays.
Police are trying to determine if the graffiti is gang-related.
Prosecutors from the Suffolk County District Attorney's Office are also investigating.
"To the perpetrators who left this mark of hate and violence on our town where our youth come to play know this, we will find you and you will be turned over to face the consequences," Supervisor of Islip Angie Carptener said.
The park is still currently open but will be closed to remove the graffiti.
It was previously the site where numerous companies illegally dumped toxic waste.
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