Essien appeared just once for Ghana in Brazil, as a second-half substitute in their 2-1 defeat to the United States last month.
He was named on the bench by head coach Kwesi Appiah for the Portugal clash in Brasilia, a match Ghana knew would be their last of the tournament.
Essien did not join in the pre-game warm-up with the squad and Appiah, who was given the full-backing of the Ghana FA [GFA] on Wednesday, confirmed that the 31-year-old's actions would be investigated.
"I was notified by my technical team that he [Essien] did not warm up though he was supposed to," he said at a news conference.
"That was some minutes before kick-off against Portugal.
"Due to the urgency of the game, we had to carry on and after that I reported his conduct to the GFA in my report for the necessary action to be taken."
The Ghana camp was plagued with alleged breaches of discipline throughout the tournament, with Essien's team-mates, Sulley Muntari and Kevin-Prince Boateng, both indefinitely suspended.
There were also reported rows over appearance fees within the squad and the head coach hopes to prevent further problems with the introduction of disciplinary contracts.
"As we look ahead, I will look for committed players and we will try not to tolerate indiscipline and anyone who will bring our efforts down," he added.
"Players who come in will be made to sign contracts to forestall any problems like it happened [in Brazil].
"The contracts will spell out clearly camp rules and all other conditions."
Ghana were eliminated from the World Cup after finishing bottom of Group G with just one point from their three matches.
