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.