Serie A's disciplinary tribunal said that Jesus was caught elbowing Juventus defender Giorgio Chiellini as they clashed waiting for a corner during Sunday's 1-1 draw.
Although the referee did not report the incident, Chiellini was knocked to the ground, the incident was spotted using video evidence and the Brazilian was banned for "violent conduct".
Jesus was banned for a further game after picking up a fourth booking in the same match while team mate Mateo Kovacic was given an automatic one-match ban after he was sent off late in a bad-tempered clash.
Fiorentina defender Savic was given the same sanction after he was dismissed during Sunday'a 1-0 defeat by Parma.
The tribunal also fined Cesena 15,000 euros (11,753 pounds) because of "insulting chants based on territorial origin" by their fans during the 4-1 home defeat to Napoli.
(Writing by Brian Homewood in Berne; editing by Justin Palmer)
