The 29-year-old, who tops the league scoring charts with 22 goals, was sent off during Sunday's draw with Athletic Bilbao following a fracas with Carlos Gurpegui and Ander Iturraspe.
Ronaldo was banned for one game for the red card, with a further two matches added for a gesture he made when leaving the pitch.
The club hoped the ban would be lifted especially in light of reports in Spanish media that referee Miguel Angel Ayza Gamez had been suspended for his performance.
Real coach Carlo Ancelotti would not comment on the referee in a news conference on Friday that was held before news of the appeal rejection was announced.
"The question of the referee being suspended has nothing to do with me," he said.
Ronaldo will also miss next week's trip to Getafe and the home game against Elche on February 22.
Sunday's draw meant Real failed to take advantage of Barcelona's second defeat of the season, leaving them third on goal difference behind the Catalan side, three points behind leaders Atletico Madrid.
Ancelotti expected Wales winger Gareth Bale to be fit for the match with fifth-placed Villarreal.
He has not played since hurting his calf a fortnight ago, the latest in a string of injuries that have forced him to miss more than half the matches since joining from Tottenham Hotspur in the close season.
Bale was a late withdrawal from the King's Cup first leg win over Atletico in midweek.
"He will play on Saturday," Ancelotti said. "When I said that Bale wouldn't play on Wednesday for fear that he could suffer a reaction ... I was telling the truth."
Real were convincing in their victory over city rivals Atletico but Ancelotti is concerned that effort might affect them against Villarreal.
"We worked hard on Wednesday. It was a game played at a high intensity and we will have to show the same work rate and concentration again," said the Italian.
"It will be difficult to do this but I have confidence in my players that they will be ready."
(Reporting by Tim Hanlon; editing by Josh Reich)
