Three of the wounded were hospitalized in critical condition, including two who were in surgery with life-threatening injuries.
The victims suffered multiple gunshot wounds that were consistent with shotgun blasts, Dr. Michael Nitzken of Wellstar Kennestone Hospital told reporters at a news conference.
The gunman, who was found dead inside the sprawling facility, worked for FedEx as a package handler, Cobb County police Sgt. Dana Pierce said.
David Titus, a FedEx truck driver, said he was just coming to work around 6 a.m. when he saw someone walk up and shoot a security guard in the abdomen outside the building. He said he could hear more gunshots after the gunman went inside.
"It was chaos," Titus said. "Everyone was running, ducking and hiding, trying to get out of there."
Authorities did not immediately offer any details about the gunman's identity or any possible motive.
FedEx clerk Liza Aiken said she was working when she heard something drop, looked to her left and saw the gunman.
"He had bullets strapped across his chest like Rambo" and held a knife, Aiken said while gathered in a nearby parking lot with other employees. Before she could continue, a woman wearing a FedEx jacket told Aiken to stop talking and led her away.
The two people in surgery were a 28-year-old man and a 52-year-old woman. The third critical victim was a 22-year-old man, Nitzken said.
Another man, 38, remained at the hospital but was stable. Two other victims - a 42-year-old woman and a 19-year-old man - were treated and released.
The facility about 25 miles north of Atlanta sorts packages and loads them onto vehicles for delivery. It's next to the general-aviation airport for suburban Cobb County.
After the attack, police blocked roads leading to the FedEx center. Dozens of workers were taken by car and bus to a skating-rink parking lot to call relatives for rides. Some family members got out of their cars and hugged the workers. Several employees said they had been told not to speak with reporters.
The company offered no details about the attack, saying only that it was "focused on the needs of our team members and cooperating with the law enforcement investigation of this tragedy."