The 27-year-old left training early on Thursday after pulling up with the complaint, with his club subsequently confirming the details of the problem.
"AC Milan informs that Jeremy Menez is suffering with swelling to the tendon in the area behind his left knee," a brief statement read.
"The player will be evaluated in the following hours."
Menez moved to San Siro from Paris Saint-Germain in the close-season, after struggling for regular first-team opportunities in the French capital.
The France international has impressed in the early weeks of the season, starting all five of Milan's matches and netting three goals.
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