The Portuguese had a second-half penalty appeal turned down by Alberto Undiano during Real Madrid’s 2-1 defeat to rivals Barcelona.
Television cameras picked up the 28-year-old then berating the match official for his decision, telling him "you are a coward".
However, the Referees’ Technical Committee (CTA) will not report Ronaldo to the Competition Committee for possible disciplinary action, after Undiano did not include it in his match report.
At the same time, though, team-mate Sergio Ramos could face action as comments made after the match that "some things you cannot fight against" will be studied by the CTA.
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