An archivist going through some 2,000 boxes at the Butler Center for Arkansas Studies found the rock in one of them, the Arkansas News reported.
"It's sort of a mystery solved," said Bobby Roberts, director of the Central Arkansas Library System.
Astronauts from the 1972 Apollo 17 mission brought back the rock and gave it to then-Gov. David Pryor in 1976, the News said.
"It has probably been there, sitting in that box, 30 years, 32 years, we're guessing," Roberts said. "We're delighted it was found and not damaged."
Roberts surmised that the rock had probably been packed by one of Clinton's staff members in 1980 when he lost his first re-election race to Republican Frank White.
Clinton defeated White two years later and served as governor for a decade before being elected president in 1992.
Roberts said he intends to give the moon rock to Gov. Mike Beebe so it can be publicly displayed.
Other states also received what came to be known as Goodwill Moon Rocks from the Apollo 17 mission, and New Jersey and Alaska are still looking for theirs, Fox News reported. The network said the rocks are estimated to be worth millions of dollars.