The Juventus defender has lashed out at the 71-year-old, who is at the center of a racism row, saying Demetrio Albertini is the only "adequate" candidate.
Tavecchio caused outrage during a speech on the influx of foreign players into the domestic game by claiming that those from Africa had merely been "eating bananas" before signing professional terms with top Serie A sides.
Up until that point, the 71-year-old had been expected to defeat Demetrio Albertini in their battle to succeed Giancarlo Abete as FIGC president but Tavecchio is now coming under mounting pressure to withdraw his candidacy.
"I read his words the day after and they left me disconcerted," Italy defender Chiellini told reporters on Sunday. "I have nothing personal against Tavecchio but, at the moment, the only adequate person for the role is Albertini.
"We mustn't let Italian football embarrass itself again. The national team is bigger than Tavecchio but we must avoid having a certain type of figure for these roles. We need a person with a certain decorum and personality to perform certain roles."
The FIGC presidential vote is scheduled for August 11.