Seven headstones at North Sunderland Cemetery, Seahouses, had blue paint sprayed on them.
Several of the headstones had words sprayed on them while others were daubed with other graffiti.
The incident is thought to have happened late on Thursday, November 26.
A Northumbria Police spokesperson said: “Today (Friday) we received a report of criminal damage at North Sunderland Cemetery, Seahouses.
“A number of headstones were reported to have been vandalised.”
The cemetery, on South Lane, is managed by North Sunderland and Seahouses Parish Council.
"The parish council is very upset and disgusted at this act of unnecessary vandalism and are doing all they can to rectify this situation,” said Cllr Sylvia Hillan.
"The parish council is trying to contact the families concerned."
Enquires are on-going and anyone with information is asked to call 101 quoting log 646 271120.