Platt was sent off by referee Gianluca Rocchi shortly after gesticulating on the touchline, has three days in which to lodge an appeal against the charge of 'improper conduct'.
City boss Roberto Mancini may prefer Platt to accept the ban if it means he only misses the final Champions League group game against Borussia Dortmund in Germany, which is a dead rubber, and only one other future European game.
City have also been handed a 12,000 euros fine for the six yellow cards they picked up against the Spanish champions.
A statement from Uefa reads: "The UEFA Control and Disciplinary Body has suspended Manchester City FC assistant coach David Platt for the next two UEFA competition matches.
"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.
"Platt was sent off by the referee for improper conduct (Article 5, Disciplinary Regulations) during last Wednesday's match between Manchester City FC and Real Madrid CF.
"Manchester City FC have also been fined €12,000 for the improper conduct of its team (five cards or more) in the same match.
"An appeal may be lodged against the verdict within three days of the dispatch of the reasoned decision."