Five-time Serie A champion Chiellini made the comments in an interview with La Repubblica before the publication of his autobiography which also talks about the Brescia striker.
"Balotelli is a negative person, with no respect for teammates," Chiellini said. "In the 2013 Confederations Cup against Brazil, he didn't give us a hand in anything, he makes you want to slap him."
Italy lost 4-2 to Brazil and just squeezed past Japan 4-3 in the early stages of the competition.
They came third after losing to Spain on penalties in the semifinal.
"For someone [supposed to be] among the top five in the world, I never even thought he could be in the top 10 or 20," Chiellini added.
"Felipe Melo was even worse. The worst of the worst. I can't stand disrespectful people, those who always want to be the opposite of others. It was always a fight with him. I also told the chiefs he was a rotten apple."
Both players responded to Chiellini, with Balotelli saying that there were many opportunities to bring up issues in person.
"If this means being a champion, then I'd rather not be one. And yet, I have never disrespected the Azzurri shirt," Balotelli said on Instagram.
"At least, I have the sincerity and the courage to say things to the face. Since 2013, you have had many opportunities to do so, acting like a real man, but you never did."
Melo, who now plays with Palmeiras, said that Chiellini's harsh words came from his jealousy of the success he had enjoyed in his career.
"Also, we beat Italy 3-0 in the 2009 Confederations Cup, which was won by Brazil. He feels envy for this. On an international level, he never won anything."
Chiellini reiterated his hatred for Inter in the interview with La Repubblica.
"I hate Inter Milan as Michael Jordan hates the Pistons," he said. "Sports hatred is what drives us to overcome the others: if we give it the right meaning, it is an essential component of sport."