The 2013 FIFA Ballon d'Or winner was given his marching orders for raising a hand to Athletic Bilbao captain Carlos Gurpegi in Sunday's 1-1 draw.
Ronaldo also clashed with Ander Iturraspe and the red card forced Real to settle for a point.
Carlo Ancelotti's side are now three points behind city rivals and league leaders Atletico Madrid in La Liga.
Gamez has not been given a top-flight match for the upcoming weekend and media reports in Spain suggest he may be on the sidelines for up to a month.
Ronaldo was suspended for three matches for the incident, with two of them coming for dissent as he left the pitch.
Real's appeal is being heard on Friday.
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