The vandalism was discovered on Wednesday at the memorial along State Highway 83 in Dennis Township, Cape May County.
Police say someone used white caulk to write a derogatory phrase on the pavers and to deface the granite monument in the center.
The memorial is in honor of Trooper Bertram Zimmerman, who died in an on-duty crash on February 5, 2004 while responding to a robbery.
The state police union is offering a $5,000 reward for information that leads to an arrest and conviction.
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Anyone with information is asked to contact Woodbine Station at 609-861-5698.
State police say anonymous tips are welcome.