Responding officers found two employees had been shot, and both were taken to a hospital, police said.
The suspected gunman was shot by police, and the suspect also was taken to a hospital, police said.
No names or conditions were immediately released. Police also have not commented about a motive.
SmileDirectClub is known primarily for working with dentists and orthodontists to sell clear aligners online as an alternative to traditional braces.
The Antioch neighborhood is about a 12-mile drive southeast of downtown Nashville.
This is a developing story and will be updated.