The shooter was fatally shot at the scene, the Louisville Metro Police Department said, but it was unclear whether from police gunfire or a self-inflicted wound.
The department identified the shooter as Connor Sturgeon, 23, who joined the downtown branch of the Old National Bank as a full-time employee last year.
Police said they responded within minutes to reports of an attacker about 8.30am on Monday at the bank office near Slugger Field baseball stadium.
Officers fired at the shooter, who was armed with a rifle, police chief Jacquelyn Gwinn-Villaroel told reporters.
The attacker broadcast live video of his attack over the internet, she said.
Police identified the dead as Joshua Barrick, 40; Thomas Elliot, 63; Juliana Farmer, 45; and James Tutt, 64.
Kentucky Governor Andy Beshear, on the verge of tears, said during a news briefing that he knew some of the victims, including Elliot, a senior vice president at the bank.
"I have a very close friend who didn't make it today," he said.
"And I have another close friend who didn't, either. And one who's at the hospital that I hope is going to make it through."
The nine people wounded in the attack were treated at the University of Louisville hospital, a hospital spokesperson said, including two police officers.
One of the police officers, a 26-year-old recent graduate of the police academy, was struck in the head and remained in critical condition after brain surgery on Monday, police said.
Two other victims were also in critical condition.
According to the Facebook page of the shooter's mother, Sturgeon grew up in Southern Indiana, which is just north of Louisville.
The elder of two boys, he attended Floyd Central High school, where he ran track and played basketball for the team that his father Todd coached.
He enrolled as a business student at the University of Alabama in 2016.
The shooter worked at the bank as an intern for three summers from 2018 to 2020 before becoming a full-time employee in 2022 as a "portfolio banker," according to a LinkedIn profile page.
He had no prior contact with Louisville police, the police chief said.
"This was a targeted act of evil violence," Craig Greenberg, mayor of the city of 625,000, told reporters at the briefing.
Greenberg said he was also friends with Elliot, who had worked on the mayoral transition campaign.
Mass shootings have become recurrent in the United States.
So far this year, the country has experienced 146 mass shootings - using the definition of four or more shot or killed, not including the shooter - according to the Gun Violence Archive, a non-profit group.
In one of the most recent high-profile incidents, three nine-year-old students and three staff members were killed by a former student at a school in Nashville, Tennessee, on March 27.
