Boos outnumbered cheers when Beckham was introduced before the game. One sign read "Hey Becks, Here Before You, Here After You, Here Despite You."
At halftime, Beckham approached the fans, made some gestures, and one of them came out of the stands toward Beckham.
Security stopped the man and police later arrested him on suspicion of trespassing, according to an officer from the California State University Dominguez Hills Police Department, which provided security for the game.
Galaxy head coach Bruce Arena said the fan has been banned from future games. According to USA Today, the stadium's policy is to permanently ban any fan who comes onto the field.
City News Service contributed to this report.