The Englishman was questioned by a supporter as he walked into the dressing rooms at The Home Depot Center regarding recent allegations of involvement with a prostitute.
The fan shouted 'stop with the prostitutes' prompting Beckham to confront him and reply with 'Do you want to say it again? Say it to my face' but the club have decided not to punish Beckham.
"We have reviewed the incident internally and determined that no action is required," said Patrick Donnelly, Galaxy's director of communications.
But it is not yet clear whether or not Beckham will receive any sanctions from MLS.
MLS' executive vice-president of communications Dan Courtemanche said that the league "reviews all aspects of every league match, including on-field competition, the fan experience, stadium operations and many other facets.
"We are currently in the process of reviewing this past weekend's matches."