Valencia's David Navarro has been suspended for seven months for his part in the brawl at the end of the UEFA Champions League match against Internazionale last week, while Carlos Marchena, Nicolas Burdisso, Maicon, Ivan Cordoba and Julio Cruz have also been given bans.
The Spanish side advanced to the quarter-finals after a 0-0 draw at the Mestalla took them past Inter on the away goals rule.
However, pandemonium broke out after the final whistle as Navarro punched Burdisso and left the Inter defender with a broken nose.
Several other players from both sides got involved as the trouble spilled over into the tunnel, and Uefa has been quick to take action.
Both clubs were charged with improper conduct and have now been fined 250,000 Swiss francs (£106,000) by Uefa's control and disciplinary committee.
A number of individuals have also been punished following the examination of official reports and video evidence.
Navarro has been hit hardest for sparking the brawl, and he will not be allowed to return to action in Europe until October.
Uefa is to ask world football's governing body Fifa to extend the suspension imposed on Navarro to international level, meaning the ban would then apply to all competitions - including domestic leagues and national team fixtures - on top of Uefa club competition matches.
Navarro's Valencia team-mate Carlos Marchena has been suspended for four European games.
Inter duo Burdisso and Maicon must serve six-game bans, while Cordoba has been suspended for three matches and Cruz for two.
Uefa has opted not to impose a stadium ban on Valencia, who meet Chelsea in the quarter-finals of the Champions League.