Among other things, the vandals dug down to Shafer's burial vault and spray painted a French phrase that translates to "Cursed for all eternity Shafer."
State police say the vandalism was found Nov. 4 at St. John's Community Church of God and the church's neighboring cemetery. Both are about 80 miles north of Pittsburgh, near Meadville.
Authorities haven't detailed what else was painted on the church or the Shafer monument, but his family has said Shafer'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.