Part of the three-piece headstone was smashed off and deep gouges cut into the granite of all three elements. The vandals also dug a hole in the surface of the gravesite, dropping a ceramic ornament from the grave into the hole.
No other headstones or gravesites were damaged.
Senior Constable Walker said the damage "would have taken considerable force" and the piece broken off the headstone is missing.
"We would appreciate any information on the whereabouts of the broken piece of headstone, or who may have been responsible."
Anyone with information can phone the Police non-emergency number, freephone 105, or call in to the Waipukurau Community Hub on Northumberland St.