Ballardini, who had been in charge for just seven games, did not coach Palermo when they beat Verona 1-0 away on Sunday in a key relegation battle.
The players said he did not speak to them either before or after the game.
Italian media reported that Ballardini was involved in a row with goalkeeper and captain Stefano Sorrentino on Saturday after trying to drop him and Zamparini intervened on the player's behalf.
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"Ballardini has fired himself, a coach cannot behave like that," Zamparini told a news conference on Monday.
"The team managed to get a result yesterday, even playing without a coach. Today, I found what I think is the best solution. As they say, sometimes bad luck doesn't cause harm."
Schelotto was previously in charge of Argentine club Lanus for three years, his first coaching job.
He spent his entire playing career in Argentina apart from a three-year stint with Columbus Crew in Major League Soccer.
Zamparini has seen 30 coaching changes in his 13 years at the helm.
Ballardini had replaced Giuseppe Iachini, who had survived for two years making him the longest-serving coach under Zamparini.
Palermo are 16th in the 20-team table with 21 points from 19 games.
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