The 59-year-old said Sulley Muntari was left with bruises and blood on his face following an altercation with a management member.
The Black Stars exited the tournament at the group stage after coming up winless in a group containing USA, Germany and Portugal.
Ghana’s campaign in Brazil was blighted by issues of delayed bonuses, with players even threatening a boycott before the country’s final group game against Portugal.
There was also an episode where midfielder Muntari clashed with a member of the FA following a fall out.
The former AC Milan and Portsmouth star reportedly exchanged blows with the said management member, later revealed to be the President of Medeama SC, Moses Armah Parker.
Recounting events that transpired that day, Appiah, who was then coaching the Black Stars, said the delay in paying player bonuses led to uncontrolled agitations.
In his autobiography, ‘Leaders Don’t Have To Yell’, the 59-year-old said an altercation between Muntari and the management member turned totally chaotic.
“I went to Sulley Muntari’s room to find out what had happened. He told me he was trying to explain something to the management team member and that turned into a heated exchange,” Appiah said in the book.
“The heated exchange led to the management member throwing a blow at him, and he retaliated by fighting back. He showed me a bruise, along with a dab of blood, that he had sustained from the incident.”
Appiah said he was later informed that the chaos started after Muntari referred to management team as liars following the delay in payment of player bonuses.
He added that, despite calming Muntari down, the player returned to the FA official’s room to vandalise his properties, including a laptop and cell phone.
Meanwhile, Muntari was later sacked from camp, together with Kevin-Prince Boateng, on the orders of the Black Stars coach.
Appiah is currently promoting his recently launched autobiography, titled 'Leaders Don't Have To Yell'.
The 400-page book is a leadership memoir in which Appiah shares his account of key events during his playing days and his two stints as coach of Ghana.