The incident occurred at a FedEx operations center near the Indianapolis International airport, after 11p.m. local time on Thursday night, according to Reuters.
Indianapolis police spokeswoman Genae Cook said the authorities had responded to a report that shots had been fired and "arrived to an active shooter incident."
"Preliminary information is that the alleged shooter has taken his own life here at the scene," she said, adding that there was no longer any threat to the community.
Four people were transported to hospitals, one in critical condition with gunshot injuries and three others with various other injuries, she said.
A FedEx spokesman said the company was "deeply shocked and saddened" by the loss of its team members. He did not clarify if all those killed were FedEx employees.
Mass shootings rise in 2021
After a significant drop in mass shootings in the United States during a pandemic-hit 2020, this year has already seen several deadly cases, according to AP.
The Gun Violence Archive says 147 mass shootings have occurred so far in 2021. Their definition of mass shooting is a minimum of four gunshot victims.
President Joe Biden last week announced a half-dozen executive actions to combat what he called an “epidemic and an international embarrassment” of gun violence in America. But he said much more is needed.
At the end of last month, four people, including a child, were shot dead in an office building in southern California.
On March 22, 10 people were killed in a shooting at a grocery store in Boulder, Colorado.
That came less than a week after a man shot and killed eight people, including six women of Asian descent, at spas in Atlanta, Georgia.
Nearly 40,000 people in the United States die each year from guns, more than half of those being suicides.
The shooting in Indianapolis came amid angry protests across the US against the police's killing of a black man over the weekend.
Protesters and police clashed for a fifth straight night in Brooklyn Center, Minnesota on Thursday, following Daunte Wright's killing by police .
Police claims that officer Kim Potter shot Daunte accidentally, having mistakenly drawn her gun instead of her Taser.
The situation in the city is tense as murder trial of the 45-year-old officer Derek Chauvin is underway there.
Chauvin, who is white, was seen in a bystander's video kneeling on the neck of George Floyd, a 46-year-old Black man in handcuffs, for more than nine minutes. Floyd’s killing sparked months of protests in the US against racism and police brutality and attracted international outrage.