"It's a heartbreaking discovery and we are working with the Council to do what we can to support these families at this time.
"At this stage our investigation team is looking into a number of avenues of inquiry, including reviewing CCTV footage from the area. We are hopeful that we will be able to find who is responsible for the damage."
Anyone with concerns about a headstone at Papakura Cemetery is urged to contact Auckland Council on 09 301 0101.
Anyone who has information on the vandalism is urged to come forward to Police.
Call Counties Manukau Police on 09 261 1300 or information can be provided anonymously to the organisation Crimestoppers on 0800 555 111.