The 25-year-old was subject to a harsh tackle during Ghana's 1-0 defeat against Libya, where he was substituted after only 22 minutes.
"Michael Essien suffered a knee injury playing for Ghana on Friday," Chelsea said in an official statement.
"He has ruptured his anterior cruciate ligament and will undergo an operation as soon as the majority of the swelling has subsided. We expect this to happen in a week's time.
"In the meantime Michael has started rehab in the aqua therapy centre at Cobham which will improve the condition of the knee prior to surgery. A return to full fitness is not expected for several months."
The combative midfielder is a key member of Luiz Felipe Scolari's team, who are currently joint leaders in the Premiership.
Prior to his injury, Essien had a groggy start to the season as he missed the Blues' first league game against Portsmouth with a leg injury.