Navarro broke the nose of Inter’s Nicolas Burdisso in the brawl.
Burdisso and teammate Douglas Maicon was banned for six games, while Ivan Cordoba and Julio Cruz received three and two-match bans.
Valencia’s Carlos Marchena was handed a four-match ban for his part in the brawl.
Both clubs were also fined £111,000 each. They will now have three days to lodge an appeal.