The Portugal forward was given his marching orders at the Nou Camp on Sunday after picking up two yellow cards - one for taking his shirt off after scoring and the other for diving.
After receiving his second yellow card, Ronaldo appeared to push referee Ricardo De Burgos Bengoetxea and was subsequently hit with a five-match suspension by the Spanish Football Federation (RFEF) - one for the double booking and another four for pushing the official.
The 32-year-old will miss the second leg of the Spanish Super Cup against Barca on Wednesday as well as Madrid's La Liga opener away at Deportivo La Coruna on Sunday.
He will also be suspended for the matches against Valencia (home), Levante (home) and Real Sociedad (away).
Real boss Zinedine Zidane branded Ronaldo's second yellow card as "ludicrous" following the victory over Barca .
He said: "I'm annoyed that Cristiano Ronaldo was sent off, it might not have been a penalty, but still, giving him a card is ludicrous.
"I am truly proud of my players, they played well as 10 and really wanted the win. Now we turn our attentions to the return leg and we need to relax."