Tavecchio, 71, was announced as the FIGC's new president earlier this month, beating Demetrio Albertini to the role, but came under fire for some of his words during his campaign.
The comments are reported to relate to a debate about scrapping limits on non-EU players in Serie A.
However, FIGC released a statement on Monday announcing the federal prosecutor had elected to end the investigation into the case.
"The federal prosecutor, having examined the stories in the press, the petitions presented, the footage acquired and the documents provided by the Italian FA to FIFA and UEFA, has dismissed the proceeding," it read.
Explaining the reasons, the statement continued: "because it did not reveal any facts of disciplinary importance to charge the newly elected President of the FIGC Carlo Tavecchio both in objective and subjective terms."
Tavecchio remains the subject of a UEFA investigation, with the European governing body revealing on Wednesday that it would look into his alleged conduct during the presidential campaign.