The striker shoved referee Ricardo de Burgos Bengoetxea after being sent off during Madrid’s 3-1 win over Barcelona in the first leg of the Spanish Super Cup final on Sunday.
Madrid appealed but that was rejected a few hours before the second leg at the Santiago Bernabeu, meaning Ronaldo misses the match as well as his team's first four La Liga fixtures.
"It's impossible not to react to this situation, 5 games! It seems to me exaggerated and ridiculous, this is called persecution!" Ronaldo wrote in an Instagram post.
The RFEF did not immediately respond to a Reuters request for comment.
Madrid could still take the case to the Spanish government’s sports court to try to reduce the ban.
Some Madrid fan groups are planning to protest against unfair refereeing, which they say their club has suffered, by waving white handkerchiefs at the second leg of the Super Cup final, according to Spanish media reports.
(Editing by Toby Davis)
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