The footage also showed a man walking through the cemetery about 6.30pm and police believe that person might have valuable information that could help the investigation.
"The person responsible for this is likely to have returned home on Saturday evening covered in dirt. Anyone who has suspicions about someone they know who may have been involved in this incident is asked to contact Police as soon as possible.
"We are working closely with Auckland Council and families to try and resolve this crime quickly and get the best result for the families who have been affected."
A mother of two children buried at the site, Ariana Simeon, said the destruction was devastating.
"We are lucky we found my children's gravesites. All the crosses and headstones were removed so some people don't even know where their children are buried," she said.
Auckland Council said it was an "appalling act of vandalism".
The council's cemeteries manager, Catherine Moore, said staff discovered the damage on Sunday.
About three or four sections of the cemetery had been damaged, including adornments thrown around and damage to headstones.
Police have increased patrols around and within the Papakura Cemetery.
Anyone with information should call Counties Manukau Police on 09 261 1300 or information can be provided anonymously to the organisation Crimestoppers on 0800 555 111.