The brawl broke out shorly after full-time in the game, which ended 2-2.
Soldado, who has yet to score in six appearances so far this season, was one of three players sent off, alongside Fenerbahce's Jailson Siqueira and Galatasaray's Badou Ndiaye.
Soldado has been banned for six games, whilst Siquiera and Ndiaye were issued with eight-match and five-match bans respectively.
Former Turkey boss Fatih Terim, currently 'Gala' manager, was also sanctioned after he insulted the referee in his post-match press conference.
Terim was banned for seven games, whilst his assistant Hasan Sas was found guilty of attacking opposition players and banned for eight games.
Finally, Galatasaray's Garry Mendes Rodrigues and Ryan Donk were banned for three and six games respectively for unsportsmanlike conduct.
Unsurprisingly, both teams were also fined for the incidents.