The male shooter opened fire late on Thursday night before shooting himself dead just after 11pm.
At least four people were taken to hospital including one with critical injures. Another two people were treated and released at the scene.
Indianapolis Metropolitan Police Department (IMPD) Officer Genae Cook described the attack as “heartbreaking”.
FedEx released a statement early Friday saying it is cooperating with authorities and working to get more information.
“We are aware of the tragic shooting at our FedEx Ground facility near the Indianapolis airport. Safety is our top priority, and our thoughts are with all those who are affected,” the statement said.
Live video from the scene showed police tape in the parking lot outside the facility and a number of emergency vehicles.
Jeremiah Miller, who works at the facility, told WISH-TV 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,” he said.
Another man said his niece had been sitting in her car when the gunfire started and had been shot.
“She got shot on her left arm,” said Parminder Singh. “She’s fine, she’s in the hospital now.”
He said his niece did not know the shooter.
Family members gathered at a local hotel to await word on loved ones. Some said employees aren’t allowed to have their phones with them while working shifts at the facility, making it difficult to contact them.
The attack in Indianapolis came after a wave of mass shootings across the United States in recent weeks:
In mid-March, eight people were shot to death at three massage parlors in the Atlanta area, raising fears that the crimes may have targeted people of Asian descent.
Less than a week later, 10 people were killed when a gunman opened fire at a grocery store in Boulder, Colorado.
At the end of March, a gunman killed four people, including a 9-year-old boy, at a real estate office in Southern California.