Simeone was sanctioned for having charged onto the pitch at the end of the match during a verbal clash with Real's French defender Raphael Varane.
He will now be absent in his side's game in their next European assignment commencing in September.
Meanwhile Xabi Alonso's penalty will serve his own punishment when his side face Sevilla, who are Europa league winners in the Uefa Super Cup final on August 12 in Cardiff, Uefa said.
In addition, Atletico and Real were each fined for improper team conduct – a penalty faced by teams who receive five or more cards during matches.
Real picked up five, thereby receiving a fine of €18 000, while Atletico's seven cards led to a penalty of €21 000.
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