The man fired one shot as he was confronted by performers who saw him fleeing with their belongings about 9:30 p.m. Tuesday at Excalibur Hotel and Casino, Las Vegas police Officer Laura Meltzer said.
No one was hit by gunfire, she said.
One cast member was treated at the scene for minor injuries after police said he was struck in the face during the scuffle, hotel spokesman Gordon Absher said.
The suspect was taken to a Las Vegas hospital with unspecified injuries pending transfer to the Clark County jail. His name wasn't immediately released.
Thunder From Down Under, an Australia-based all-male group featuring chiseled shirtless men, has wowed millions of viewers, mostly women, since 1991.
Hotel operations and the show schedule weren't affected by the scuffle, said Absher, a spokesman for hotel owner MGM Resorts International.
A Thunder From Down Under executive didn't immediately respond to messages.