Ronaldo was sent off in bizarre fashion, collecting a yellow card for taking his shirt off during a goal celebration before being shown a second for alleged diving.
Ten-man Real thrash Barcelona at Camp Nou
Upset by referee Ricardo De Burgos Bengoetxea's decision to dismiss him, Ronaldo shoved the official, which landed him in further hot water.
RFEF issued Ronaldo with a €3,005 fine and a four-match suspension in addition to the automatic one-game ban the player was due to serve for his red card.
Ronaldo, who struck a spectacular second goal for a dominant Madrid, will miss the Super Cup second leg at the Santiago Bernabeu on Wednesday and the club's first four La Liga matches.
Isco stars in Real’s Super Cup triumph
Having featured in the Confederations Cup for Portugal, the striker only returned to training earlier this month.
He came on as a substitute in the UEFA Super Cup win over Manchester United on August 8.
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