The employee was helping guests down from the wires as thunderstorms rolled into the area.
Museum officials reported that the worker touched a piece of equipment that had been charged by a lighting strike and the electrical current ran through his body.
He was taken to a nearby hospital, but his injuries were said to be superficial.
The zip lines were installed earlier this year to help the Christian-themed museum attract a wider group of visitors.
The 1,700 feet of cable are suspended 150 feet above the ground at their highest point.
The accident took place at 1 p.m. Wednesday, and the zip lines were closed for the rest of the day.