Witness video shows airport police detaining the woman and searching her bags. Earlier in the incident, the woman was seen being combative as employees tried to stop her while they waited for officers to arrive.
"Airline employees who witnessed the woman exiting the terminal followed security protocols and maintained visual contact until the airport police arrived shortly thereafter and detained the woman," LAX said in a statement.
An alarm went off when the woman went out the door at Terminal 1 around 6:30 p.m.
LAX said she told police she was trying to flag down a plane, which was still parked in the gate area.
Journalist Tezlyn Figaro said she was waiting to board a Southwest flight when she saw a commotion outside the window at Terminal 1. She said the woman ran out a door and onto the tarmac to stop a plane.
The woman was taken into custody and transported to a hospital for minor injuries and for a mental health evaluation.