Jacksonville Sheriff Mike Williams said authorities believe 24-year-old David Katz of Baltimore carried out the attack using at least one handgun at the Jacksonville Landing, a collection of restaurants and shops along the St Johns River.
He said the man died from a self-inflicted gunshot and that authorities were still making final confirmation of his identity with the FBI assisting them in Baltimore.
Nine other people were wounded by gunfire and all were in stable condition on Sunday evening, Sheriff Williams said.
He added that two others were injured in the chaos as people sought to flee the gunfire.
Katz was in Jacksonville for the Madden NFL 19 video game tournament.
The competition was held in a gaming bar that shares space with a pizzeria. Viewers could watch the games online and see the players.
Investigators were looking into online video that appeared to capture the scene right before the shooting began, the sheriff said.
A red dot that appears to be a laser pointer is visible on the chest of a player seconds before the first of a dozen gunshots rings out.
Marquis Williams, 28, and his girlfriend, Taylor Poindexter, 26, both from Chicago, were ordering pizza at the bar when they heard the gunfire.
Mr Williams said people trampled each other in the panic while trying to get away.
“Initially we thought it was a balloon popping, but there weren’t any balloons in the room. Then we heard repeat shots and we took off running,” said Mr Williams, who participated in the tournament earlier.
Jason Lake, the founder and chief executive of compLexity, a company that owns professional e-sports teams, said on Twitter that one of his players, 19-year-old Drini Gjoka, was shot in the thumb.
Gjoka tweeted: “The tourney just got shot up. Im leavinng and never coming back.” Then: “I am literally so lucky. The bullet hit my thumb. Worst day of my life.”
The sheriff’s office used Twitter and Facebook immediately after the shooting to warn people to stay far away and to ask anyone who was hiding to call 911.
Police also barricaded a three-block radius around the shopping centre. Officers and Coast Guard boats patrolled the nearby river.
Many ambulances could be seen in the area, but the shopping centre area appeared empty of all but law enforcement. Police also took up positions on a bridge overlooking the river.
On Sunday evening, the FBI said its agents searched a family home of the man authorities believed was behind the attack.
Heavily armed agents, some in bulletproof vests and brandishing long guns, could be seen entering an upscale townhome complex near Baltimore’s Inner Harbour.
An FBI spokesman, Dave Fitz, confirmed that agents had gone to the house of the man’s father in Baltimore.
He declined to release specifics, citing the ongoing investigation.
TJ Smith, chief spokesman for the Baltimore Police Department, also said that the agency was assisting law enforcement partners “with some information that has led authorities to Baltimore”.
White House spokeswoman Sarah Huckabee Sanders said President Donald Trump had been briefed on the attack and the White House was monitoring the situation.
The Jacksonville Landing, in the heart of the city’s downtown, also hosts concerts and other entertainment. It was the site of a Trump rally in 2015, early in his campaign for the White House.