The names of the victims or gunman were not immediately released.
“The (shooter) came into the parking lot, and I believe he left his vehicle and started shooting quickly … The first shooting took place in the parking lot, and then he went in and didn’t get far (inside),” Indianapolis Police Deputy Chief Craig McCartt told CNN early Friday.
Police arrived “in a very chaotic scene, with victims and witnesses all over the place,” McCartt said.
McCartt said he believes the shooter committed suicide when officers met him. No police officer fired, he said.
The motive for the shooting was not immediately known, Indianapolis police spokeswoman Genae Cook said.
At least four survivors were taken to a hospital with gunshot wounds, as was someone with an injury believed to have been caused by shrapnel, McCartt said.
One person was in critical condition, police said.
The shooter had at least one weapon – “some sort of gun” – and investigators were trying to determine if he had more, McCartt said.
Friday police tried to make sense of the crime scene, while relatives of FedEx employees gathered at a nearby hotel to wait for news about their loved ones.
‘I thought I was going to be shot’
At first, Jeremiah Miller and Timothy Boillat thought the sound was coming from a car, but after hearing more, Miller got up and saw a man with a gun, he said.
“After hearing the shootings, I saw a body on the floor behind a vehicle,” Boillat said. The two men left the building and watched as about 30 police cars responded.
“Thank goodness you were here because I thought I was going to be shot,” Miller told the station.
Police are asking anyone who was on the scene and may have left for safety or medical treatment to contact them for information about the shooting.
FedEx said in a statement it was aware of the “tragic shooting” at the Indianapolis facility.
“Safety is our top priority, and our thoughts are with all concerned. We are working to gather more information and work with investigative authorities,” spokesman Jim Masilak said in an email to CNN.
“I am communicating with the local authorities to get full details of the attack and my office is ready to assist all those affected in any way possible.”
CNN’s Joe Sutton and Keith Allen contributed to this report.