Someone spray-painted "Black lives matter" on the granite marker on West Chapel Hill Street near Duke University.
The words "Tear it down" were spray-painted on the other side.
The monument was installed in May by the Sons of Confederate Veterans. About 40 Confederate soldiers are buried at the site.
A representative of the group was at the cemetery Wednesday afternoon to begin the cleanup.
"To vent hatred by damaging a marker is not a good thing to do, especially in a cemetery," said Sons of Confederate Veterans member Stewart Dunaway.
Dunaway said he's concerned about things that are representative of history being torn down.
"I think it's a great concern that citizens need to talk about since the horrific event in South Carolina. And the issues that are going on down there with the flag and the state capitol should bring the discussion back to citizens and I would really call on everyone to understand all aspects of the Civil War," he said.
"I think that weirdo in South Carolina that did that horrific event, having a Confederate flag, is just as wrong as a person who says a Confederate flag only means slavery, needs to be burnt and destroyed, and removed from everything. That's just wrong," he continued.
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