A part of the metal fence several metres wide was found broken on the grass at Market Drayton Cemetery, on the side bordering Cemetery Road.
Market Drayton Town Council has committed funds to replace the damaged section, but deputy mayor Councillor Roger Smith said that what caused the damage might never be discovered.
"I have asked one or two of the people living close by and they didn't hear anything at all," he said.
"It is a strange one because the wall that the fence is on is a stone wall and it's quite high really. My first thought was that some vehicle has reversed into it.
"On second thought though, it's a difficult one with the wall being so high – it would have to be a reasonably high vehicle to have caused that damage and not hit the wall beneath.
"If it's vandals I don't know how they would have managed it either.
"I don't think we're going to find out what's caused it to be honest."