Television images captured De Rossi delivering the blow, which was not seen by referee Mauro Bergonzi, late in the first half of Saturday's 0-0 draw at the Stadio Olimpico.
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The 30-year-old was suspended on Monday and will now miss matches against Napoli, Udinese and Chievo.
"The television replays show that the Roma player aggressively pushed (the) opposition player's head," a statement read.
"Then, in quick succession, he punched Icardi with the same hand from behind.
"The resolution is to sanction the player with a three-match ban."
Inter's Juan Jesus has received the same punishment after punching Alessio Romagnoli in the back during Saturday's fixture.
Meanwhile, Italy head coach Cesare Prandelli has defended his decision to omit De Rossi for the friendly encounter with Spain.
Prandelli has taken a dim view of De Rossi's conduct and has warned that any player who fails to follow his "code of ethics" will not feature, regardless of their role in the team.
"The code of ethics is our regulation," said Prandelli at his pre-match press conference. "From the first day of the season, if I have seen something that I deem inappropriate, I will not call up that player.
"With De Rossi, I saw it on television and decided. The lad has accepted the decision.
"I don't want any crazy things happening in (the FIFA World Cup in) Brazil, so this is a warning."
Prandelli has opted to take Giorgio Chiellini to Madrid for Wednesday's friendly despite the Juventus centre-back struggling for fitness following a calf injury.
Juve boss Antonio Conte voiced his concerns over the call-up, but Prandelli has defended the decision.
He added: "During all these years we've always had a good relationship with Juventus. That hasn't changed.
"Even if a player is on the bench, I have the right to call him up.
"Yesterday, the Juve doctor sent us a message saying that all the players were okay, and that Giorgio had trained normally."