The score was already tied at 1-1 when Ronaldo was shown the eighth red card of his career after clashing with Athletic midfielders Ander Iturraspe and Carlos Gurpegui 15 minutes from time.
The Spanish Football Federation handed the Portuguese the normal one game ban for a straight red card, but also added an extra two games for a gesture of dissent Ronaldo made as he left the field.
Madrid still have the option to appeal the ban, but, should it be upheld, Ronaldo will be ruled out of the La Liga fixtures against Villarreal, Getafe and Elche.
However, the former Manchester United man will be free to take part in Wednesday's Copa del Rey semi-final, first leg at home to Atletico Madrid as the suspension only applies to league fixtures.
Atletico currently lead La Liga by three points from both Madrid and Barcelona, who are locked on 54 points with 16 games still to go.