Airport officials also confirmed that Terminal 3 will remain closed.
A police officer said the shooting suspect, 23-year-old Paul Ciancia, was carrying a hand-written note which said he said he wanted to kill Transportation Safety Administration workers.
The official told the Associated press the note said he "wanted to kill TSA and pigs."
President Barack Obama said he is "concerned" about the shooting at Los Angeles airport, although he declined to comment on the details of the incident.
"We're concerned about it, but I'll let law enforcement folks talk about it directly," Obama told reporters in the Oval Office, Washington.
Law enforcement officials have identified the LA airport shooting suspect as 23-year-old Paul Ciancia, the Associated Press has reported.
A spokesperson for UCLA Medical Center in Los Angeles confirmed that of the three patients they received following the shooting in LAX Airport, one is in a critical condition and two are in a fair condition.
Chief of Los Angeles Airport Police Patrick Gannon said his officers engaged the shooter inside terminal three after he fired numerous shots, and managed to arrest him.
One person, a man approximately 40 years old, was killed in a shooting at Los Angeles International Airport on Friday, a spokesman for the Los Angeles County Coroner said.
The suspect in the Los Angeles International Airport shooting appeared to be acting alone and was using an assault rifle, police have confirmed.
Speaking at a press conference, the Chief of the Los Angeles Airport Police Patrick Gannon said: "An individual came into Terminal 3 of this airport, pulled an assault rifle out of a bag and begun to open fire in the terminal.
"He proceeded up into the screening area where Transportation Security Administration (TSA) screeners are and continued shooting and went past the screeners back into the airport itself.
"Officers from Los Angeles Airport Police responded immediately to the calls. They tracked the individual through the airport and engaged him in gunfire in Terminal 3 and were able to successfully take him into custody."
Seven people were wounded in the shooting at Los Angeles International Airport and six of them were taken to local hospitals for treatment, a Los Angeles fire department spokesman said.
The gunman invovled in the LAX Airport shooting has been taken into custody and is believed to be a lone shooter, the chief of airport police Patrick Gannon has confirmed.