"After hearing the appeal CONMEBOL decided to reduce the sanction ... to two games," the organisation explained in a statement.
The suspension still means Jara will miss Monday's Copa America semi-final against Peru and the final or third/fourth-place playoff.
The player's fine was also reduced from $7,500 to $5,000.
Jara received his ban for "unsporting behaviour" after he stuck his finger up Cavani's backside in the quarter-final win over Uruguay last week.
Cavani responded to the provocation with the slightest of touches and Jara fell to the ground theatrically, prompting the referee to send the Uruguayan off.
Chile scored the only goal of the game soon after.
A second Uruguayan was shown a red card two minutes before the final whistle, leading to scuffles between players and officials from both sides.
CONMEBOL said it would decide after the tournament whether to sanction Uruguayan players for their part in the incidents.
Paraguay face Argentina in the second semi-final on Tuesday.
(Reporting by Andrew Downie, editing by Tony Ji9menez)
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