Biglia recently joined the Rossoneri from Lazio as part of an extensive summer spending spree in the Italian capital, as Milan seek to rebuild their squad under chairman Li Yonghong.
The Argentina international last featured for Milan during their International Champions Cup victory over Bayern Munich, but has not made an appearance for the club since.
"After today's tests, Lucas Biglia was diagnosed with a lesion to his left thigh femoral bicep muscle," the club confirmed in a statement on Friday. "His time of recovery will depend on the evolution of the clinical picture and is estimated to be approximately four weeks."
It is thought that Biglia will now have to wait until the middle of September before making his Serie A debut for Milan.