Team spokesperson Ward Zouhair told The Associated Press that Chedli "wasn't happy" at not being in the team and left Tunisia's base in Franceville on Wednesday morning, four days ahead of the country's quarter-final.
Zouhair said the 35-year-old veteran, who won the African Cup with Tunisia in 2004, was in the Gabon capital Libreville waiting for a flight home and would not play any further part at the tournament.
"Once a player decides he is not happy and wants to go home, you can't do anything about it," Zouhair said.
Zouhair added there was no problem with Chedli during Tuesday's 1-0 loss to Gabon at Stade de Franceville despite reports he was sent to the stands by coach Sami Trabelsi after becoming angry that he wasn't in the team.
Chedli was even left out when Trabelsi made a host of changes for the game against Gabon after the team had already qualified for the last eight.
Chedli became the second player to exit the tournament in 24 hours, after Clifford Mulenga was expelled from Zambia's squad and sent home for breaking a curfew and showing no remorse. Two other Zambia players, who had also stayed out late, had apologised and were allowed to stay with the squad.
Tunisia play the Group D winners - who are expected to be Ghana - in the quarter-finals on Sunday. Zambia faces Sudan in the last eight on Saturday.