Ex-Ghana forward Boateng, 28, played 59 minutes of the Bundesliga match while Germany winger Sam, 27, was absent.
The club, managed by former Chelsea boss Roberto Di Matteo, blamed a "lack of mutual trust" and told both players they can find new teams.
Midfielder Marco Hoger, who played the full 90 minutes against Cologne, has been suspended for a week.
Hoger, 25, joined the club from Alemannia Aachen in 2011.
Sam was signed last summer from Bayer Leverkusen on a four-year contract while former Tottenham and Portsmouth player Boateng joined from AC Milan in 2013 on a three-year deal.
A club statement read: "Schalke sporting director Horst Heldt announced there would be consequences after Sunday's defeat away to Cologne and the first action taken has been: Kevin-Prince Boateng and Sidney Sam have been suspended with immediate effect.
"Marco Hoger is suspended from training and first-team action up to and including Saturday, 16 May."
Schalke, who lost to Real Madrid in the Champions League last 16, still have two games remaining of the Bundesliga season.
Schalke have suspended Kevin-Prince Boateng and Sidney Sam indefinitely following Sunday's 2-0 loss at Cologne.