The measure, House Bill 91, is designed to safeguard statues, plaques and other markers recognizing revolutionary or Confederate heroes from modern sensibilities that may object to views on race held in the 18th and 19th centuries.
Rep. Tommy Benton, R-Jefferson, introduced the proposal at the request of the Sons of the American Revolution and the Sons of Confederate Veterans.
The bill, if passed, would require that monuments be kept in a prominent place.
"We're not saying they can't move them," Benton said. "We're just saying they can't just put them in a field somewhere."
He also introduced a separate bill that would require property owners to give access to the families of people buried in private cemeteries on their land. He said many families have been frustrated that they can't get permission to tend the graves of their ancestors because those who now own the land surrounding the family plots refuse.