Police said they stopped a suspected stolen vehicle near Terminal 3 around 9 a.m., and one person was arrested while four others were detained for questioning and then released.
Larry McKenney, 35, of Humboldt, Texas, was arrested on suspicion of possession of a stolen car and possession of methamphetamines in a custodial setting.
To try and control the scene, officers moved people off sidewalks and into the baggage claim. Some travelers who saw police with their guns drawn panicked and backtracked through security-screening areas. LAX officer Rob Pedragon said about 15 people left out of an emergency exit and onto a tarmac.
Police quickly brought the scared passengers back inside, and Terminal 3 was then evacuated as a precaution.
Between 1,500 and 2,000 travelers went through a second security check, and a total of 18 flights were delayed.
L.A. Mayor Eric Garcetti issued a statement in which he confirmed the public was not in danger, but said he understands why people panicked.
The statement read in part: "I understand that events around the world have caused travelers everywhere to have a heightened level of concern for their safety. The millions of people whose journeys begin, end, or pass through LAX should know that it has the finest, most prepared airport police force and federal security personnel in the nation - and that their safety and protection will always be our number-one priority."
The evacuation came a week after 911 calls falsely reported gunshots at LAX, which sent people running onto streets and the tarmac.
The Associated Press contributed to this report.