The Ghana international came on for Sulley Muntari at half-time of Milan's comprehensive 3-0 victory over Chievo on Saturday.
However, Essien - who moved to San Siro from Premier League outfit Chelsea in January - is now unlikely to feature against Genoa on Monday or Catania on April 13, as the Serie A club assess the extent of his injury.
"AC Milan wishes to communicate that Michael Essien has picked up an injury to his right thigh," a statement on the club's official website read.
"The player will undergo further tests in 10 days' time."
Essien has made six appearances in Serie A for Milan, who have endured a tough campaign and sit 11th in the table with seven games remaining.
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