The gunman was identified as a local 51-year-old man and was pronounced dead at the scene, police spokesman Don Aaron told reporters.
"The only person who was shot was the suspect as he emerged out of the rear door of the single movie theater," he said.
Aaron said police officers working an accident scene nearby quickly responded to the reports of a gunman at the theater. One of them entered the cinema, encountered the gunman and "may well have saved multiple individuals inside."
When confronted, the gunman fired at the officer, who then returned fire and waited for backup.
The gunman appeared to be shot dead in a hail of bullets when he tried to exit the cinema and encountered police, a witness said.
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"There was dust flying everywhere," said plumber Sean Oliver, who heard a volley of shots and was able to see the back of the cinema.
Three people were treated for exposure to pepper spray, including a 58-year-old man who also suffered a superficial wound to his shoulder, likely from the ax, Brian Haas of the Nashville Fire Department told reporters. None of the victims was taken to hospitals.
"This could have been a lot worse," Haas said.
The man also had a backpack strapped to his chest that police said they later detonated to eliminate any possible threat.
The shooting comes less than two weeks after three people were killed and nine were wounded when a gunman opened fire in a cinema in Lafayette, Louisiana. The gunman was among the dead.
The incident was on the minds of many in Tennessee.
"This makes me want to hug my mother," said Calvin Johnson, 17, who was at a restaurant about 50 yards from the shooting.
Two employees of a nearby Starbucks restaurant said they heard three or four gunshots and saw several police cars, fire trucks and ambulances responding.
The Tennessee and Louisiana shootings come three years after 12 people were slain and dozens wounded by a gunman at a cinema in Aurora, Colorado, during a midnight screening of the Batman film "The Dark Knight Rises."
