Authorities identified 19-year-old Geddy L. Kramer of Acworth as the shooter. His body was found near a shotgun, Pierce said.
"That was the only weapon that he had at that time," Pierce said.
The warehouse is located in Kennesaw, Georgia, about 21 miles northwest of downtown Atlanta.
"Numerous" 911 calls from inside the half-million-square-foot package and delivery facility alerted police to the shooting at 5:54 a.m., Pierce said.
The victims were taken to WellStar Kennestone Hospital, where an emergency room doctor involved in the response said three were in critical condition.
EMS officials warned the hospital at 6:26 a.m. to prepare for the victims' arrival, Dr. Michael Nitzken said. By 7 a.m., the six patients -- all of whom had suffered multiple gunshot wounds -- had arrived.
Without naming them, Nitzken identified them as:
-- a 28-year-old man in critical condition after undergoing surgery;
-- a 52-year-old woman in stable condition after undergoing surgery;
-- a 22-year-old man in stable condition;
-- a 38-year-old man in stable condition;
-- a 42-year-old woman who was treated and released;
-- a 19-year-old man who was treated and was to be released.
Two of the patients -- the 28-year-old man and the 52-year-old woman -- suffered life-threatening injuries and the man was placed on mechanical ventilation, he said. "They appeared to be shotgun blast effects, with multiple, small projectiles," Nitzken said.
Their arrival at the level-two trauma center coincided with a shift change. "That proved to be to our benefit," the doctor said, because the staff was double what it typically would be. "We're trying to make the best of a bad outcome."
FedEx spokesman Scott Fielder told CNN that the situation had stabilized "and we are focused on the needs of our team members and cooperating with the law enforcement investigation of this tragedy."