Department spokesperson Genae Cook said when officers arrived they "came in contact with an active shooter incident" and enetered the building while the gunman was still shooting.
Indianapolis State Police Sgt John Perrine said Interstate 70 near the facility was closed in both directions.
Investigators from IMPD and Indiana State Police are still seeking a motive.
At least four were hospitalised, including one person with critical injuries.
Multiple other people were injured and went to local hospitals, police spokesperson Cook said at a news conference.
Ms Cook said two others were treated at the facility by the medical staff and released and that "multiple" others had walked in to hospitals in nearby areas.
"I am communicating with local authorities to get all details of the attack and my office stands ready to help everyone affected in any way we can", he said.
Jeremiah Miller had finished a shift at the FedEx facility and was preparing to work a second consecutive shift when he and a coworker, Timothy Boillat, heard gunfire, up to 10 shots. No law enforcement officers were injured.
At first Jeremiah Miller and Timothy Boillat thought the sound was from a auto, but after hearing more, Miller stood up and saw a man with a weapon, he told the station.
Footage from the scene shows police tape in the auto park outside and multiple emergency service vehicles. She said there was a shooting in the FedEx.
One witness who who said he worked at the facility told WISH-TV he saw a man with a gun after hearing several gunshots.
In a statement, FedEx said it was aware of the "tragic shooting" at the Indianapolis facility.
"We are working to gather more information and are cooperating with investigating authorities", he added.
"She got shot on her left arm", Parminder Singh said.