The Italy international was forced to limp off during the first half of Milan's 0-0 Champions League draw with Ajax, and scans have since shown that the problem relates to an injury sustained earlier in the season.
Injuries have limited El Shaarawy to just four Serie A appearances so far this campaign, meaning that the latest news comes as a blow following his first start since August.
The 21-year-old found the net on 18 occasions for Massimiliano Allegri's side last season, but the club announced that they will be without his services over the Christmas period.
"During the match against Ajax, Stephen El Shaarawy suffered a pain in his left foot," read a statement on AC Milan's official website.
"He will need a period of rest of about two or three weeks."