The Brazil international received a straight red card for the 90th-minute incident that came moments after he had given away a penalty for a foul on Sergej Milinkovic-Savic during Sunday’s Serie A game.
The penalty was missed but Antonio Candreva scored on the rebound to secure 10th-placed Lazio a 2-1 win over table-topping Inter.
Melo now misses the away games against Empoli and Atalanta on January 6 and 16 respectively, and the home clash with Sassuolo at the San Siro on January 10.
“Unfortunately, Melo did two stupid things,” said Inter coach Roberto Mancini after the match.
Mancini added that the result had “ruined Christmas” and that his side were not the favourites to win the title as a result.
“We levelled the scoring and then threw away the game again. Lazio’s winning goal was the result of stupidity,” said the former Manchester City boss.
“This game has ruined Christmas a bit, but we are still first. Juventus, Napoli, Fiorentina and Roma are the favourites.”