The Transportation Security Administration confirmed one of its employees had been shot.
Emergency vehicles and heavily armed police are on the scene and have established a triage area. Officers were searching the terminals.
Passengers have evacuated the airport, some onto the tarmac.
LA Police spokeswoman Norma Eisenman told reporters a suspect had been arrested after opening fire inside Terminal 3.
Norma Eisenman said multiple people were wounded. Their condition is not currently known.
The Federal Aviation Administration (FAA) has barred all flights landing at the airport, and outbound flights have been delayed.
The incident was initially reported after 9:30 local time.
The LA Fire Department said it was assisting police at a “multi-patient incident”.
Witness Brian Keech, told the Associated Press news agency he heard “about a dozen gunshots” from inside the security gate at Terminal 3.
The White House confirmed President Barack Obama had been briefed on the incident.
Authorities are scheduled to hold a press conference at 11:30 PST.
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