A mysterious granite structure that has long drawn tourists to a cow pasture in rural Georgia sustained heavy damage Wednesday when someone set off an explosive device, according to law-enforcement investigators.

The “Georgia Guidestones,” a 19-foot-three-inch tall Stonehenge-like monument outside of Elberton, Ga., partially collapsed after the explosion at about 4 a.m., according to a Georgia Bureau of Investigation spokeswoman. No one was injured.

The Guidestones have drawn attention and criticism to Elbert County, in northeastern Georgia not far from South Carolina, since they were unveiled in 1980. The murky origins of the 119-ton monument and the odd messages inscribed on its monoliths in various modern and ancient languages are part of its appeal to many tourists.

The monument has been promoted locally as a tourist attraction but tagged as a road map for an apocalypse by conspiracy theorists.

Photo: Cameron McWhirter/The Wall Street Journal

No one has ever publicly disclosed who designed and paid for the Guidestones. The slabs are arranged in a county-owned pasture to serve as an astronomical calendar. Each stone bears messages to humanity. While locals have promoted the monument as a tourist attraction, conspiracy discussion groups on the Internet have viewed the monument as a warning or road map for an apocalypse. One inscription declares the Earth should only have 500 million people. The current global population is about 7.8 billion, according to the World Bank.

Earlier this year, Kandiss Taylor, a Republican gubernatorial candidate, made the destruction of the Guidestones a platform of her campaign, claiming the monument was evil. She lost the primary, receiving about 3.4% of the vote. The Guidestones have been vandalized repeatedly over the years, and the county installed security cameras at the site.

The secretive group that paid for the monument wanted to point humanity to a new “Age of Reason” and care for the planet, according to an official account of the monument’s creation. Joe Fendley Sr., who headed a granite company, led the construction of the monument and never revealed the identity of the monument’s sponsor. Mr. Fendley, who became Elberton’s mayor, died in 2005.

His daughter, Melissa Caruso, a real-estate agent in Elberton, said Wednesday that her father would be heartbroken. “It’s a sad day for Elbert County,” she said. “The Guidestones were a legacy for my family.”

Write to Cameron McWhirter at cameron.mcwhirter@wsj.com