The suspect was shot dead as he tried to escape
With a rucksack on his chest and wearing a surgical mask, the man was shot dead by officers while trying to escape after carrying out the attack.
One person suffered a ?superficial? hatchet wound and three people were treated for exposure to pepper spray.
The man was later named as a 29-year-old local, Vincente David Montano.
Police spokesman Don Aaron said Montano had ?significant? psychological issues and had been committed to psychiatric care four times.
He had also been arrested in 2004 for assault and resisting arrest.
Police had at first believed the attacker was 51. They also mistakenly said he had a firearm but later clarified it was a pellet gun.
Officers were called at 13:13 local time (17:13 GMT) on Wednesday to the Carmike Hickory 8 cinema in Antioch, where a screening of Mad Max: Fury Road 2D was just starting.
Witnesses were running out as the police arrived, and one officer entered the auditorium through the projection room, only to be shot at by the gunman.
The assailant tried to escape out of a rear door but was shot dead.
His rucksack, still strapped to him when he died, was detonated by authorities and ?nothing of danger? was found, police said.
Nearby businesses were placed on temporary lockdown.
The latest attack comes about two weeks after a shooting at a cinema in Lafayette, Louisiana.
And jurors in Colorado are currently deciding whether the man who killed 12 and injured 70 during a Batman film in 2012 should receive the death penalty.
BBC