Rodrigo Bentancur was banned for four games, while Ronald Araujo, Jose Maria Gimenez, and Mathias Olivera each received three-game suspensions.
After Colombia sealed a 1-0 victory in the Copa semi-final, Uruguay players climbed into the stands and exchanged blows with opposition fans.
Uruguay captain Gimenez said the players were trying to defend their families.
The Uruguay FA was also fined $20,000, and 11 players in total were sanctioned for their involvement in the brawl. Nunez was fined $20,000, Bentancur $16,000, and Araujo, Olivera, and Gimenez $12,000 each.
The players will have to serve their suspensions in Uruguay's next official matches in their 2026 World Cup qualifiers.
They face Paraguay in Montevideo and Venezuela in Maturin in September; Peru (away) and Ecuador (home) in October; Colombia (home) and Brazil (away) in November.