Núñez was among the players who entered the stands at the Bank of America Stadium and exchanged punches with fighting fans during the chaotic conclusion of the game.
The forward received the most severe punishment, with others facing suspensions of four matches or less, alongside fines.
Midfielder Rodrigo Bentancur, who plays for Tottenham in England, was suspended for four matches, while defenders Mathías Olivera, Ronald Araújo, and José María Giménez were each banned for three matches.
Núñez was fined $20,000, with the other players receiving fines ranging from $16,000 to $5,000.
Six other players received fines only.
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