One headstone has been ripped out, a plaque has been removed from another grave, and ornaments and vases broken at others.
Waitaki District Council staff reported the damage to police on Wednesday, but it is understood it occurred sometime over the past three weeks.
Council parks officer Mike Kwant said five graves were damaged.
The cost of the damage was more than $1000, but the emotional harm to family members of the deceased would be hard to quantify, he said.
Council staff were still trying to contact some family members to tell them about the damage.
The damage would have taken some time and effort to inflict, he said.
"Usually, vandalism is quick and easy. So, from a theft perspective, [this is] highly unusual and people usually have a respect for the dead. Human behaviour doesn't usually go that low, particularly in places like Oamaru.''
The damage appeared to be random, rather than targeted at any particular graves, he said.
Anyone who had seen any suspicious activity in or near the cemetery in the past three weeks was asked to contact the Oamaru police.
