Several headstones were toppled over and a large number of ceramic vases smashed at Kinloss Abbey where a section of the original abbey wall was also pushed over.
The damage was discovered on Tuesday by Moray Council workmen carrying out maintenance at the burial ground.
The ruins of the abbey, which dates from the 12th century, are a scheduled ancient monument and grade A listed building and have been the subject of conservation work in recent years.
A spokesman for Moray Council said: “The headstones which were toppled are not believed to have been badly damaged and attempts will be made to contact the lair holders. A six-metre length of one-metre high wall was pushed over and will require specialist restoration, while it is estimated that between 20 and 30 ceramic flower holders were removed from graves and smashed against a section of wall.”
He added: “It is thought the damage may have taken place over the weekend and Police Scotland have been informed.”