Cobb County Police Sgt. Dana Pierce said that an unidentified male suspect arrived at the facility around 5:45 a.m. and started shooting, according to Atlanta news station WXIA.
The suspect since died of a self-inflicted gunshot wound, according to police.
The six people injured were taken to a hospital in neighboring Marietta, Ga., according to CNN. One victim was in surgery.
A company spokesman said FedEx was aware of the incident.
"The primary concern is the safety and well-being of our team members, first responders and others affected," spokesman Scott Fielder said, as quoted by CNN. "FedEx is cooperating with authorities."
This post has been updated. Image via WGCL