Evra sat out Sunday's 2-0 win over Palermo, having suffered the injury in training ahead of the clash.
And coach Massimiliano Allegri will now have to do without the experienced campaigner for upcoming crunch matches against Olympiacos in the UEFA Champions League and Lazio in Serie A.
A club statement read: "Patrice Evra was absent from the group [training on Monday] following the injury he sustained late last week.
"The Frenchman underwent medical tests earlier today which revealed a strain of the biceps femoris muscle [hamstring] in his left thigh, and he is estimated to return to action in 30 days."
Evra has made six appearances since moving to Turin from Manchester United in the close-season.
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