Authorities say eight people have been killed, not including the shooter, while 60 people have been injured, including 20 with gunshot wounds.
The gunman also took his own life and police said they believe there is no longer an active threat to the community.
Officers were called to reports of gunfire just after 11pm and arrived to an active shooting situation.
Investigators are working to gather information on the suspect, who has not yet been identified.
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It is also unclear what the motive was behind the attack and whether the gunman worked at the facility.
Footage from the scene shows police tape in the car park outside and multiple emergency service vehicles.
Family members have gathered at a local hotel to wait for word on their loved ones.
A witness, who said he works at the facility, told WISH-TV that he saw a man with a gun after hearing several gunshots.
“I saw a man with a submachine gun of some sort, an automatic rifle, and he was firing in the open,” said Jeremiah Miller.
Another witness said his niece was sitting in her car when the gunfire began.
“She got shot on her left arm,” said Parminder Singh. “She’s fine, she’s in the hospital now.”
His niece had said she did not know the gunman.
Indianapolis Police officer Genae Cook said: “Today it is very heartbreaking and, you know, in the Annapolis Metro Police Department, the officers responded, they came in, they went in and they did their job.”
The FedEx facility is close to Indianapolis International Airport.
A spokesperson for the delivery service said the company was aware of the incident and was “working to gather more information”.
US Congressman Andre Carson, a representative for Indiana, said he was “heartbroken” following the attack and was “praying for all affected by this tragedy”.
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“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.