Platt will not be allowed in the dugout for City's final Champions League group game next Tuesday against Borussia Dortmund.
He was charged with improper conduct by UEFA's Control and Disciplinary Body following his dismissal by the referee during the 1-1 draw with Real.
"The UEFA Control and Disciplinary Body has suspended Manchester City FC assistant coach David Platt for the next two UEFA competition matches," a UEFA statement read.
"He will not be able to carry out his function at Tuesday's UEFA Champions League Group D match against Borussia Dortmund in Germany, as well as at the next UEFA competition match for which he will be eligible."
UEFA, European soccer's governing body, said Manchester City had also been fined 12,000 euros ($15,500)for the improper conduct of its team after five players received yellow cards.
The club have three days to appeal the decision.
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