The Ghanaian picked up a muscle strain in his side's victory over Chievo at the weekend and is now awaiting further tests to determine the full extend of the damage
However, Essien - who moved to San Siro from Premier League outfit Chelsea in January - is now unlikely to feature against Genoa on Monday or in the clash with Catania on April 13, as the Serie A side assess the full extent of the damage.
"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 league appearances for Milan, who have endured a tough campaign and currently sit 11th in the table with just seven games remaining.