Biglia suffered the injury in his right leg and missed Milan's last-gasp victory over Udinese in Serie A on Monday (AEDT) as the Rossoneri evaluated the severity of the problem.
Scans confirmed surgery was required to fix the issue, and Biglia was operated on in Finland.
Biglia's operation was a success, Milan confirmed in the build-up to their Europa League clash with Real Betis, but he faces a lengthy recovery.
"The injury suffered by Lucas Biglia last Wednesday during the morning training session involved the lesion of the myotendinous junction of the medial segment of the right calf," a Milan statement read.
"The operation, carried out today in Finland by professor Sakari Orava in the presence of the team doctor Stefano Mazzoni, was successful.
"Full healing will take four months."