Evans' appeal was heard on Tuesday by former NFL wide receiver James Thrash, who was jointly appointed by the NFL and the NFLPA.
It its ruling, the league stated that Evans' suspension without pay comes due to "violations of unnecessary roughness and unsportsmanlike conduct rules."
The fracas began with an altercation between Buccaneers quarterback Tom Brady and running back Leonard Fournette, and Saints defensive backs Marshon Lattimore and Marcus Maye, with Fournette and Lattimore shoving each other. Evans ran into the fray and blindsided Lattimore with a heavy shove that escalated the fight.
Evans and Lattimore were ejected from the game, which Tampa Bay won, 20-10. Evans previously was suspended in 2017 for one game following another incident with Lattimore.
Evans, 29, has eight receptions for 132 yards and a touchdown over two games this season.