It was alleged during Brighton's match at West Brom on January 13 that Rodriguez had used abusive and/or insulting words which included a reference to ethnic origin and/or colour and/or race.
However, the charge has been found not proven following an Independent Regulatory Commission hearing.
Rodriguez requested a personal hearing this week and in a statement following the ruling, The FA said: "The FA wishes to stress that there has been no suggestion by any party involved in this case that this was a malicious or fabricated complaint. The FA is completely satisfied that this was a complaint made in absolute good faith.
"The FA takes all allegations of discrimination extremely seriously and continues to encourage all participants who believe that they have been the subject of or witness to discriminatory abuse to report this through the appropriate channels.
"The FA would like to express its full thanks to all parties for their full cooperation during the disciplinary process."
West Brom director of football administration Richard Garlick said: “Everyone at the Club is delighted for Jay because this has been a trying period for him.
“He has always maintained his innocence and we are naturally pleased the Commission has dismissed the charge.”