Vettel directed pointed remarks towards FIA race director Charlie Whiting and Red Bull driver Max Verstappen in the closing stages of the Grand Prix following a tense battle with the Dutchman.
However, in a statement issued on Tuesday the FIA said that Vettel had "spontaneously sought out Charlie Whiting to express his regrets for his behaviour in person."
"He then, again on his own initiative, sent letters to each of the FIA President Jean Todt and Charlie Whiting, in which he apologised profusely for his actions," the statement continued. "He also indicated that he would likewise be contacting Max Verstappen and vowed that such an incident would never occur again.
"In the light of this sincere apology and strong commitment, the FIA President has decided, on an exceptional basis, not to take disciplinary action against Mr Vettel by bringing this matter before the FIA International Tribunal.
"The FIA will always condemn the use of offensive language in motor sport – especially when directed at officials and/or fellow participants – and expects all participants in its Championships to be respectful and mindful of the example they set for the public and the younger generation in particular.
"The FIA takes this opportunity to advise that, in the event of any future incident similar to the one that occurred in Mexico, disciplinary action will be taken by bringing such incident before the FIA International Tribunal to be judged."
