State police in Meadville announced the vandalism in a news release, but didn't offer specifics.
The Meadville Tribune reports Tuesday that Shafer's daughter, Diane Shafer Domnick, confirms that her father's grave was targeted in the vandalism at St. John's Community Church of God and the church's neighboring cemetery. Both are about 80 miles north of Pittsburgh, near Meadville.
Domnick and police haven't said what was painted on the church or the Shafer monument, but she says her "father's accomplishments were targeted."
Shafer died in 2006 and served as governor from 1967 to 1971.
He was also a prosecutor, state senator, lieutenant governor and served in the Nixon administration.