Menez, who joined Milan from Paris Saint-Germain in June, has made a strong start to his career at San Siro, scoring three goals in six Serie A games.
However, the 27-year-old could be set for a spell on the sidelines in what would be a blow to Milan's hopes of continuing their relatively impressive early season form under Filippo Inzaghi.
A statement on Milan's official website read: "AC Milan would like to communicate that Jeremy Menez is suffering from a problem to his right adductor muscle. The player will undergo further tests over the next few days."
With Milan's next fixture at Verona a week on Sunday, Inzaghi will hope that Menez has enough time to recover from the problem.
The 18-time Italian champions sit fifth in Serie A, having taken 11 points from their first six games.
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