Police named the suspect as 19-year-old Brandon Hole, who last worked at the company in 2020.
He began shooting "randomly" almost immediately after exiting his car, according to police.
Seven people were also injured and the gunman apparently killed himself before police arrived, officials say.
This is the latest incident in a recent uptick of mass shootings across the US.
The victims in Thursday's shootings have not yet been named.
A statement from FedEx chairman and CEO Frederick Smith described the incident as a "senseless act of violence".