Police said the 35-year-old "Terminator 2" and "American History X" star was arrested on the arrivals level of Terminal 2 about 12:45 a.m., the Los Angeles Times reported.
His arrest took place after airport police received a call about a "possible domestic violence investigation," Sgt. Belinda Nettles said in a statement.
Furlong was booked and jailed in lieu of $50,000 bail, the newspaper said.
In 2007, he was charged with public intoxication following his arrest at a grocery store in Kentucky, and last year he was arrested on suspicion of violating a restraining order requiring him to stay away from his estranged wife, the Times said.