The identity of the person killed was not disclosed.
"Our thoughts and deepest condolences are with the [crew member's] family at this time," the film studio said in a statement Wednesday. "The safety of our cast and crew is our top priority and the studio is fully cooperating with all investigating agencies as they examine the circumstances surrounding this unusual accident."
Paramount did not provide details regarding the circumstances of Tuesday's incident, but TMZ quoted unnamed sources as saying the man was fatally injured while working on a high-powered scissor lift when the machine tipped. He had been helping to tear down the set, the entertainment news Web site said.
The film stars Bruce Willis, Dwayne Johnson and Channing Tatum. It is being directed by Jon Chu and is set for a 2012 release. "G.I. Joe 2: Retaliation" is a sequel to 2009's "G.I. Joe: The Rise of Cobra."