According to airport police, the man left through one of the security doors at the Tom Bradley International Terminal around 8 p.m. Wednesday. Officers followed him onto the tarmac.
Video from the scene shows him scurrying just feet away from a Singapore Airlines plane near a runway.
Officers tried to detain him, but the suspect didn't cooperate. They used less-than-lethal force to take him into custody.
Airport officials say the man suffered minor injuries and had to be hospitalized. He appeared to be under the influence of a substance.
Additional details were not available.