The ban was given to him by Conmebol after he clashed with fans at the end of Uruguay's Copa America semifinal against Colombia last year.
Nunez had already served two matches of the ban before the Court of Arbitration for Sport agreed to hear his appeal. However, his appeal has been rejected.
According to the Court of Arbitration for Sport, Nunez's actions were not justified and did not meet the standards of self-defence.
The Court stated that Nunez's conduct was voluntary, violent, and unjustified, and therefore violated Conmebol's disciplinary code.