The deadly attack happened at the facility on Mirabel Road in Indianapolis, near Indianapolis international airport, late on Thursday night.
Indianapolis police department spokesperson Genae Cook said the male shooter is believed to have taken his own life, saying there was no longer any “active threat” to the community.
Multiple other people were injured in the mass shooting and were taken to hospital, Ms Cook added – with one person said to be critically ill.
A witness who works at the FedEx facility told WISH-TV that he saw a man with a gun after hearing 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 said.
Another man told WTTV that his niece was sitting in her car in the driver’s seat when gunfire erupted. “She got shot on her left arm,” said Parminder Singh. “She’s fine, she’s in the hospital now.”
Mr Singh added that his niece did not know the shooter.
FedEx earlier said it was cooperating with authorities, adding: “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.”
Ian Johnston, whose wife works at the facility, told reporters she had been in contact. “My wife works in there and she texted me to tell me there’s an active shooter and we communicated back and forth for a while, she’s since notified me she’s okay.”
He added: “After I communicated with her for a while, then it went silent for a while, so I came here just to see what was going on and she texted me I’m okay.”
Family members with loved ones who work at the FedEx facility were told by the Indianapolis Metropolitan Police to gather at the Holiday Inn Express hotel, about a mile from the FedEx facility.
Ashlee Floyd, whose father has been working at the facility for two decades, was woken up by a call from her nephew in New Mexico who saw the news about the incident on television.
“I’m just worried about my father. I don’t know if he’s ok. I don’t know if he’s injured. I don’t know if he’s gone. I’m just scared right now. I don’t know anything. Nobody knows anything,” Ms Floyd told the Indianapolis Star.
She emphasised that it is her father who usually calls his wife’s phone at 11:25 p.m or "normally when my mom calls, he’ll answer with his watch, but he has not responded. So we are kind of concerned.”
The lack of any information about their loved ones working at the centre is what was worrying the families the most.
Ashley Ladd, whose 22-year-old daughter, Shayla, works as a manager at the facility, said that “nobody knew what was going on” but she was lucky to know within five minutes that she was alright.
She was alerted by a phone app about the shooting following which she immediately connected with her daughter via a video call during which she said red and blue police lights flashed across her face and people were heard screaming.
Curtis Carson, whose roommate worked at the FedEx, was told that he was safe. “I just feel sorry for the families, man. Indianapolis is big for shootings and violence, but this takes the cake,” said Mr Carson.
Some said employees aren’t allowed to have their phones with them while working shifts at the facility, making it difficult to contact them.
Police were expected to give another update on Friday morning, but the exact time of a news conference wasn’t immediately available.
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