Thirteen bronze plaques have been stolen from Makara cemetery cemetery near Wellington.
Police fear they will be sold as scrap and will be speak to scrap metal and second-hand dealers.
Wellington City Council says the theft is a despicable and disrespectful thing to do.
Officials are contacting descendants of the deceased.
The plaques were found to be missing on Wednesday, but it's believed they were taken over the weekend.
The council says it has photographs of the plaques and will be able to replicate the information if they don't turn up.