Referee Miguel Ayza Gamez gave the Portuguese star his marching orders after the incident, with the official later adding that the card was not just for the incident with Gurpegui but also his entanglement with Athletic's Ander Iturraspe.
Gamez is said to have initially told his fellow officials that Ronaldo was sent off for raising his hand to Gurpegi but has reportedly since changed his story.
Real Madrid are understood to be angry with the change in reasoning, and have 10 days to appeal the red card.
The RFEF's official judgement says that Ronaldo received a one-match ban for the red-card incident and tangling with Iturraspe, plus an additional two-game ban for an "offensive gesture" following his dismissal.
He will miss the Liga clashes against Villarreal, Elche and Getafe, but remains available for the Copa del Rey clash with Atletico Madrid.
Ronaldo - who celebrated his 29th birthday on Wednesday - was also fined 1,200 euros (£1,000), with Real being fined 1,050 euros.