It is the second time this year that the JSPCA Animals Shelter pet cemetery has been targeted.
Eight headstones were pulled up and left lying on the ground following the the attack.
The damage was discovered on Tuesday morning by Bryan Ferey, who manages the site.
It is thought that the vandals struck the previous night and the police want to speak to anyone who might have any information about the incident.
The headstones have now been put back in place, and staff at the Animals Shelter were this morning still trying to contact those whose pets are buried in the cemetery.