At least three other people, including a second TSA employee, were wounded, NBC News reported citing federal authorities. But it was not clear whether the shooter was among the injured.
President Barack Obama has been briefed on the shooting and will continue to be updated, White House spokesman Jay Carney told reporters. But the official said he had no further information on what happened at the moment.
The shooting happened at about 9.20 in the morning (9.50 p.m. India time) at Terminal 3 at a screening station where fliers show their IDs and boarding passes, NBC News said citing Nico Melendez, a TSA spokesman. The agent was shot in the leg, he said.
The suspect wearing military-like clothing and carrying a rifle approached the checkpoint at terminal 3 and shot a TSA officer, CBS News reported citing a law enforcement source.
Authorities believe the event is not widespread and is over, the channel said.
Aerial video showed what appeared to be a TSA employee being wheeled away into an ambulance by police. Several people were seen being treated by emergency responders outside the terminal, but it's unclear if they are gunshot victims, it said.
Nick Pugh told NBC that he was waiting in line for security on the upper mezzanine when he heard eight to 10 shots.
"We were just standing there in line and somebody started shooting," he was quoted as saying. "Everyone dropped to the floor and started crawling along the ground, abandoning their suitcases."
Passenger Robert Perez told CBS that TSA agents came through the terminal and yelled that a man had a gun.
"I heard popping and everybody dropped to the ground," Perez said.
Another witness told MSNBC that there was an initial round of shots, then a pause, then more shots. An airline worker told them, "Go out! Go out!" the witness said. People streamed down the stairs and onto the tarmac for safety, he said.
The Federal Aviation Administration grounded flights taking off from Los Angeles and those that were bound for Los Angeles and had not already taken off.