Ronaldo handed two-match ban
The Portuguese netted a first-half double at the Bernabeu but was shown a straight red card in the 70th minute for lashing out at Patrick Mtiliga and breaking the Malaga defender's nose.
Real, who had asked for the card to be rescinded, are likely to appeal against the ruling but if that is rejected Ronaldo will miss Saturday's trip to Deportivo Coruna and the home game against Espanyol the following weekend.
The RFEF's disciplinary committee decided his behaviour was not wilful or reckless, which would have meant a longer suspension, but that he had been guilty of dangerous play.
Real were also fined 180 euros, the RFEF said on their website.
Ronaldo apologised to Mtiliga immediately after Sunday's game but said the red card was "a disgrace."
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 earlier been booked for taking off his shirt in a goal celebration.
Dane Mtiliga will almost certainly miss Malaga's match at Atletico Madrid on Sunday and will have to wear a protective mask when he returns to action, the club said on their website.