The Chelsea midfielder has been struggling with injury and has been told he will not fully recover until the end of July.
The GFA said that the decision was taken after a joint evaluation of his fitness by them and his club.
His last competitive match was for Ghana during the Africa Cup of Nations earlier this year.
He took part in the early stages of that tournament despite not being fully fit, having torn a hamstring in December.
He then injured his knee and has not played for either Ghana or Chelsea since.
Essien has been keen to play down speculation about his chances of making the World Cup.
"If I make it for the World Cup then great - if not I have my whole career ahead of me," he told Chelsea's official website in April.
"The last thing I want is to rush back and cause more problems down the line."
Ghana coach Milovan Rajevac had been publicly optimistic but also insisted that the squad can still succeed without Essien.
"There are other young and hungry players who will be equally passionate to play," he said recently.
Ghana are in Group D at the World Cup, along with Germany, Australia and Serbia.
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