The midfielder also was fined $1,500.
The foul came in the 38th minute of a 1-0 Real Salt Lake victory Saturday.
Major League Soccer's disciplinary committee followed up the red flag by penalizing Mondaini, saying he "was reckless and endangered the safety of his opponent."
"The existence of a serious injury alone does not mandate supplemental discipline of a certain level," Nelson Rodriguez, MLS executive vice president of competition, technical and game operations, said on the league's Web site in explaining why even greater punishment was not administered.
"The circumstances of each play are examined in great detail and discussed at length."
Morales had surgery Monday and it's possible he could return before the end of the season.
He is the third MLS star to suffer serious injury this season. Seattle Sounders FC winger Steve Zakuani suffered a broken tibia and fibula and 2010 MVP David Ferreira suffered a broken ankle.
Colorado Rapids midfielder Brian Mullan received a 10-match suspension for fouling Zakuani on the play on which he was hurt.
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