The man entered the Greenwood Park Mall with a rifle and several magazines of ammunition and began firing in the food court, Greenwood Police Department Chief Jim Ison said.
An armed civilian killed the man, Ison said at a news conference. In total, four people were killed and two were injured, he said.
Officers went to the mall at about 6 pm for reports of the shooting. Authorities are searching the mall for any other victims, but they believe the shooting was contained to the food court.
Police have confiscated a suspicious backpack that was in a bathroom near the food court, Ison said.
Indianapolis Metropolitan Police and multiple other agencies are assisting in the investigation.
"We are sickened by yet another type of incident like this in our country," Indianapolis Assistant Chief of Police Chris Bailey said.
There is no active threat to the area, Bailey said.
Greenwood is a south suburb of Indianapolis with a population of about 60,000. Mayor Mark Myers asked for "prayers to the victims and our first responders."
"This tragedy hits at the core of our community," Myers said in a statement.
Authorities said they would provide more details Sunday night.