Peterson, 36, is accused of verbally and physically assaulting his wife on a plane that was leaving for Houston, where he lives.
According to the Los Angeles County Sheriff's Department, Peterson was arrested at about 9 a.m. and was booked a couple of hours later. He posted a $50,000 bond and was released.
His wife remained on the flight, police said. According to several posts on Peterson's Twitter account, he and his wife had been in Los Angeles for events surrounding the Super Bowl.
Peterson is charged with domestic violence, according to police.
The star NFL running back has been charged in the past. In November 2014, Peterson pleaded guilty to a misdemeanor reckless assault charge after he admitted to hitting his 4-year-old son with a switch at his home in The Woodlands as a form of discipline. As part of a plea agreement, Peterson was sentenced to two years probation with a number of conditions.
Peterson, a native of Palestine, Texas, played his college ball at Oklahoma. He broke into the NFL in 2007 with the Minnesota Vikings. He played 10 seasons in Minnesota before stints in New Orleans, Arizona, Washington, Detroit, and most recently, Seattle.
A spokesperson for Peterson told TMZ it was a verbal argument and it was a private misunderstanding.