De Rossi, who was also omitted from Italy's squad, was seen to punch Inter forward Mauro Icardi in the cheek in an off-the-ball incident as the two tussled in the penalty area, Serie A's disciplinary tribunal said.
Juan Jesus punched Roma's Alessio Romagnoli in the back in a separate incident, the tribunal said.
Both players were punished on the basis of video evidence as the cases were not included in the referee's report, it added.
Sassuolo forward Domenico Berardi was also given a three-match ban for his sending-off against Parma, which happened only 48 seconds after he had come on as a substitute.
Berardi, 19, was dismissed for elbowing an opponent in the 72nd minute of Parma's 1-0 win on Sunday.
Italy coach Cesare Prandelli does not tolerate bad behaviour by his players and routinely drops those who get into trouble in domestic games.
De Rossi was missing from the list on Sunday when Prandelli named his squad for Wednesday's friendly away to Spain, the third time the volatile midfielder has fallen foul of the rules.
Forwards Mario Balotelli and Pablo Daniel Osvaldo have also been left out in the past.
"I've told the players that I watch the games and I don't wait for the tribunal's decisions," Prandelli told reporters on Monday.
"I've said that if I see behaviour which crosses the line, the player will not be in the national team. I don't want tempestuous behaviour at the World Cup."
- Sports & Recreation
- De Rossi
- Mauro Icardi
- Domenico Berardi