They were understood to show that he has suffered a partially torn medial collateral ligament in his left knee and damage to his meniscus.
Essien will miss Chelsea's Premier League clash against title rivals Arsenal at Stamford Bridge on 7 February and the opening leg of their Champions League tie against Jose Mourinho's Inter Milan on 24 February.
The midfielder had only just returned to training on 6 January, having not played since tearing his hamstring while on Champions League duty with his club in early December.
The midfielder watched Ghana beat 10-man Burkina Faso 1-0 on Tuesday to advance to the Africa Cup of Nations quarter-finals before returning to London.
Ancelotti cannot guarantee games for Joe Cole
Meanwhile, Ancelotti insists that Joe Cole will remain a Chelsea player next season, even though he cannot guarantee him regular first-team football.
Cole's contract expires in the summer and the England midfielder, 28, is yet to agree a new deal with the main stumbling block understood to be his desire to play more.
Ancelotti said: "I cannot guarantee to Joe Cole that he'll play for Chelsea in every game.
"I never guarantee that to my players, even the big players. How can a manager guarantee that to the players? That's impossible.
"I don't have any news on his contract. He will stay at Chelsea next year. I'm 100% clear."
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