Sheahan said the nightclub was open at the time and the shooter was believed to have acted alone. He was hospitalized with unspecified injuries.
Sheahan said the male patron was shot and killed trying to subdue the gunman as people ran from the club.
"The person is in custody. The weapon is in custody," Sheahan said. No names have been released.
Authorities said the gunman paid an unspecified cover charge then demanded his money back before the shooting began.
The club is located on the lower level of Bally's.
Gambling continued in the casino after the shooting, but yellow crime scene tape stretched around several banks of slot machines outside the nightclub. Debris littered the floor.
The Strip was the scene of a dramatic shooting and explosion last winter. Authorities say verbal sparring erupted into a shooting, chase and crash that left three people dead in February. A death penalty trial is set for Dec. 2 against a man who once bragged about his lifestyle as a pimp.