The Italy international has played only seven games for the Serie A outfit this season after suffering thigh and foot problems, and the club have now confirmed he will be out of action until at least March.
"With everyone at the club and all the fans wishing him the best, Stephan El Shaarawy will be away from the football pitch for around 10 weeks after surgery on his foot today," said a statement on www.acmilan.com.
"Twenty-year-old El Shaarawy has already shown what he's capable of on the football pitch.
"In what must be a tough moment for the young player, Stephan should focus on the fact that time is on his side and also that when he gets back playing in three months' time, the team will be in action in the league and will need the best that the player can offer.
"And as we've all seen, he has a lot to offer.
"From all the fans waiting to see him on the pitch again, 'Forza Stephan'."
The Rossoneri currently sit in 13th in the Serie A table but are through to the last 16 of the Champions League with El Shaarawy almost certain to miss the first leg of their tie with Atletico Madrid.