Valencia's David Navarro has been banned for seven months for sparking the brawl at the end of the UEFA Champions League match with Inter Milan eight days ago.
Both clubs have been fined 250,000 Swiss francs by UEFA's control and disciplinary committee. Five other players have also been punished, Europe's governing body said.
Inter defenders Nicolas Burdisso and Maicon have been banned for six UEFA club competition matches and Valencia defender Carlos Marchena for four.
Inter defender Ivan Cordoba and striker Julio Cruz have received three and two-match bans respectively.
Navarro, 26, prompted extraordinary scenes at the end of Valencia's Champions League first knockout round victory on away goals at the Mestalla.
The Valencia substitute defender has said he was ashamed by his behaviour after running on to the pitch and punching Inter's Burdisso in the face and breaking his nose.
He was then chased by Milan players as pandemonium ensued.
UEFA said in its ruling posted on its website on Wednesday that it would ask world football's governing body FIFA to extend the suspension imposed on Navarro to international level.
It would then apply to all competitions -- including domestic leagues and national team fixtures -- on top of UEFA club competition matches.
