The World Player of the Year received an automatic one- match ban for his dismissal on Sunday and an extra four games for his reaction towards referee Ricardo de Burgos Bengoetxea.
Ronaldo was also fined USD 4,500 and has 10 days to appeal the ban.
Should any appeal fail, Ronaldo will miss Wednesday's Super Cup, second leg and Madrid's first four La Liga games of the season against Deportivo la Coruna, Valencia, Levante and Real Sociedad.
"Ronaldo's sending-off annoys me because even if it is not a penalty, the card is harsh," said Madrid boss Zinedine Zidane after the game.
"We will see if we can do something so that he is available on Wednesday."
Ronaldo was only on the field for 24 minutes as he was introduced as a second-half substitute and fired into the top corner 10 minutes from time to give Madrid a 2-1 lead.
"Once shown the red card, said player (Ronaldo) pushed me lightly as a sign of his disapproval," de Burgos Bengoetxea wrote in his referee's report.
According to the RFEF's rules, such offences are met with a suspension of anything between four and 12 games, but previous cases also resulted in four-game bans.
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