The shooting took place at Smile Direct Club shortly before 6am on Tuesday morning, when a male employee went into the building during a shift change and opened fire.
Following the attack, a man carrying a weapon and believed to be the shooter was spotted by police close to where the incident took place.
The suspect left the building as officers responded to the attack, but he was spotted at a nearby intersection.
After telling the man to drop his weapon, police fired at the suspect. Nashville Police Department spokesman Don Aaron said the man pointed his weapon towards the officers instead of dropping it.
He added that the suspect, identified as 22-year-old Antonio King, was pronounced dead after being taken to Vanderbilt University Medical Center.
The suspected gunman was armed with a semi-automatic pistol with an extended magazine, Mr Aaron said.
Two officers discharged their weapons towards Mr King. Police think the suspect was acting alone and have yet to release a possible motive behind the attack.
Authorities said the three people with gunshot wounds were all taken to hospital alive, but one of them was in critical condition. The injured employees have not been identified. One was shot in the leg, one in the abdomen, and a third was shot in the chest. One employee injured an ankle as they were running.
Two of those shot were security guards employed by Allied Universal Security and the third was an employee of SmileDirectClub, WKRN reported.
Police said that Mr King had only been working at the company since June, but had been employed there previously, between late 2019 and early 2020, according to the Nashville Tennessean.
Fire department spokesman Joseph Pleasant said five people were taken by EMTs to hospitals in the area.
Mr Aaron said neither of the officers who fired at the suspect were injured by gunfire themselves, but an investigation is ongoing following reports that Mr King may have fired his weapon at the officers.
The Tennessee Bureau of Investigation will take over the investigation as it is a police-involved shooting. Special agents and forensic scientists were at the scene of the shooting at 8.30am.
People were asked to avoid the area, which includes a number of single-story homes, as the investigation was continuing.
Smile Direct Club produces teeth-straightening products and has had its headquarters in Nashville since 2016.
“SmileDirectClub is saddened at the incident that took place at its manufacturing facilities this morning,” the company said in a statement.
“The incident was contained quickly by security personnel on-site. The safety of our team members is a top priority for our company and we maintain strict security protocols. We are working with the local police as they investigate this matter.”
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