Referee Rajindraparsad Seechurn gave Equatorial Guinea a controversial penalty in stoppage time as they beat Tunisia 2-1 in the quarter-finals.
Tunisia staff confronted the official after the match and their federation has been fined $50,000 (£33,000).
"The referees committee noted the poor performance of the referee," the Confederation of African Football said.
Caf added that the referee's failings included an "unacceptable failure to maintain calm and ensure proper control of the players during the match".
Caf also wants an apology from Tunisia for accusations of bias.
And Tunisia have been ordered to pay for damages to a door and a refrigerator in the team's dressing room at Bata Stadium.
Mauritian referee Seechurn awarded the penalty in stoppage time after Ali Maaloul was harshly ruled to have fouled Ivan Bolado when Tunisia were leading 1-0 and, after equalising from the spot through Javier Balboa, hosts Equatorial Guinea went on to win in extra-time.
Seechurn has also been removed from Caf's list of elite referees.
According to Caf, it was sent two letters by the Tunisian FA following the match, with the second asking for an investigation and suggesting that Caf and its officials "were questionable and biased against Tunisia in general".
Unless Tunisia's football federation can provide "irrefutable evidence to substantiate the accusations" they need to send a letter of apology by midnight on 5 February or face expulsion from the 2017 Africa Cup of Nations.
Tunisia football chief Wadie Jary resigned from Caf in protest after the match and he was also "condemned" for his behaviour after going on to the pitch to confront Seechurn, as well as criticising the referee and African football's governing body.
Equatorial Guinea were fined $5,000 (£3,300) for poor security at the stadium.
An Africa Cup of Nations referee has been banned for six months for "poor performance".