The 20-year-old has been struggling with injury for the past few months, which has interrupted his preparations ahead of the new season.
His one appearance so far came in the second leg of the Champions League playoff against PSV Endhoven.
The Italian international went under the knife at La Madonnina clinic in Milan earlier today, with the Rossoneri stating: "The prognosis is around a month, without complications."
De Sciglio is now likely miss Serie A games against Torino, Napoli, Bologna and Sampdoria, while also being ruled doubtful for the clash with Italian champions Juventus on October 6.
He is also expected to miss the Champions League games against Celtic and Ajax.