The left lung was taken in Peru from "Bodies: The Exhibition," which has traveled the globe displaying cadavers preserved through a process that replaces water in biological tissues with polymers.
The organ disappeared from an area where visitors can touch preserved cadavers.
"In the whole world this has never happened," said Susan Hoefken, manager of Lima-based Impacto, the company presenting the exhibition.
A $2,000 reward _ no questions asked _ was offered Tuesday for the return of the lung. It has no commercial value but will be costly to replace, Hoefken said.
She described the embarrassment of reporting the Monday theft to the show's owner, Atlanta-based Premier Exhibitions.
"They told us to recover the lung somehow," Hoefken said.
The exhibition travels next to Colombia.