Essien out of Cup of Nations
Chelsea's Essien picked up the injury in training on Sunday and medical checks showed the injury was worse than first thought.
"He will not be able to play in the tournament anymore," Randy Abbey said. "We still don't know the exact extent of the injury."
Ghana, who started their campaign with a 3-1 defeat by Ivory Coast, must beat Burkina Faso in their last Group B game on Tuesday if they are to qualify for the quarter-finals.
Essien, who had been out for a month with a hamstring injury, joined his team mates late in Angola after bad weather had delayed his departure from London.
He took part in one training session and played only 45 minutes against Ivory Coast last Friday.