Juan was not punished by match officials following a first-half clash with Giorgio Chiellini during Inter's 1-1 draw with Serie A champions Juventus on Tuesday.
However, the Brazilian has now been sanctioned by Lega Serie A for "violent conduct", with video evidence showing he had made contact with Chiellini in a crowded penalty area.
Juan was handed a three-match ban for that offence and will also miss a further game after being shown a fourth yellow card of the season later in the same game.
Savic has been handed the same punishment as a result of his late dismissal in Fiorentina's 1-0 loss at Parma, as well as also receiving a fourth booking of the campaign.
The Montenegro defender received a red card for elbowing Antonio Cassano and now faces a lengthy spell on the sidelines.
Cesena were also punished by the Italian league's governing body on Wednesday.
Serie A's bottom club have been fined €15,000 for "insulting chants based on territorial origin" during their 4-1 defeat to Napoli.
