After considering Real's arguments, the federation's appeals committee ruled that the ban and a 600-euro fine for the Portuguese forward should stand, the RFEF said on its website.
Real said in a statement on their website they would take the case to Spain's Sporting Disciplinary Committee (CEDD), a body overseen by the government sports council (CSD).
That could mean the suspension is put on hold and Ronaldo would then be available to coach Manuel Pellegrini for Saturday's trip to fifth-placed Deportivo La Coruna.
Ronaldo was shown a straight red card in Sunday's 2-0 win over Malaga after catching defender Patrick Mtiliga with a flailing arm and breaking his nose.
The RFEF's disciplinary committee decided Ronaldo's actions were not wilful or reckless, which would have meant a longer suspension, but that he had been guilty of dangerous play.
Ronaldo apologised to Mtiliga immediately after the game but said the red card was "a disgrace" and insisted he never tried to hurt another player.
It was his second dismissal of the season following his sending-off against Almeria in December for kicking out at an opponent after he had been booked for taking off his shirt in a goal celebration.
