Cavani flicked his hand in Jara???s face during the quarter-final clash and earned a second yellow card following provocation from the former West Brom player.
Jara was later banned for three matches after video evidence showed him poking a finger up the Paris St Germain striker’s backside.
The 29-year-old defender???s club Mainz responded by placing him on the transfer list.
In a bad-tempered match, the later dismissal of Jorge Fucile sparked a benches-clearing brawl which saw Uruguay coach Oscar Tabarez sent to the stands and both he and his assistant Mario Rebollo have been handed three-match touchline bans.
All three will miss the World Cup qualifiers against Bolivia and Colombia on October 8 and 12, with the coaching duo also missing November’s clash with Ecuador.
A statement from South American governing body CONMEBOL read: “CONMEBOL has communicated to the Uruguayan Football Association the decisions of the disciplinary tribunal with regard to the dismissals during the Copa America quarter-finals between Chile and Uruguay.
“Oscar Tabarez and Mario Rebollo have been suspended for three official matches. They will not be able to access the dressing room, tunnel or technical area, nor have any communication with their team before or during the match.
“Edinson Cavani was suspended for two official matches in qualification for Russia 2018.”