Directors at the Dubuque facility said someone climbed the 4-foot-tall glass wall this week and walked off with Cashew the tortoise, KCRG-TV, Cedar Rapids, reported Thursday.
"It could have been in a backpack or a large shopping bag or wrapped it in a coat," Executive Director Jerry Enzler said.
Enzler said Cashew was part of an exhibit featuring more than 60 turtle species.
Gail DeMoss, owner of New Earth Animal in Galena, said a tortoise like Cashew can fetch up to $2,000 on the black market.
Enzler said the museum was more concerned about the animal's well-being than about her worth.
"Whoever has it, we hope would call the museum and return it or at a minimum find out what's the best approach to keep the animal alive," Enzler said.