The forward received two yellow cards in this season's first El Clasico, the first after removing his shirt to celebrate scoring, and the second for supposedly diving in the Barcelona box.
On top of the one-game ban for the red card, Ronaldo will miss four further games for pushing referee Ricardo De Burgos Bengoetxea as he left the field.
Real had appealed, but on Wednesday the Royal Spanish Football Federation (RFEF) appeals committee upheld the ban.
Madrid wins despite Ronaldo red
Ronaldo had quite the eventful game Sunday, scoring a stunning goal, celebrating topless, and then the red card -- all in just 23 minutes after coming on as a second-half substitute.
The hotly-contested Spanish Super Cup clash, which pitted last season's La Liga champions against the winners of the Copa del Rey, had four goals in an action-packed second half.
Gerard Pique slid Marcelo's cross into his own net to give Madrid the lead.
Ronaldo got on the scoresheet when he curled a shot past Marc-André ter Stegen shortly after Lionel Messi had equalized from the penalty spot for the hosts.
The Portuguese was subsequently booked for taking his top off -- supposedly mimicking a Messi celebration
from last season's El Clasico -- and minutes later received a second yellow when he was adjudged to have dived in the Barcelona penalty area.
"We played a great game but I am annoyed by Cristiano's sending-off," said Real coach Zinedine Zidane.
"Perhaps it wasn't a penalty but the red card is a little harsh."
A superb 25-yard strike from Marco Asensio ensures Madrid goes into Wednesday's second leg at the Bernabéu with a two-goal advantage.
Neymar finds his feet
While Barcelona adjusts to life without Neymar, the Brazilian took little time getting acclimatized to France's Ligue 1 as he made his much-anticipated debut for Paris-Saint Germain.
He was instrumental in PSG's 3-0 victory away at Guingamp, feeding Edison Cavani with a precise chip for his side's second goal before tapping in for a score of his own in the closing stages.
The striker, watched on by his father, showed few signs that he was struggling to make himself at home in France.
He had six shots and completed 88 passes, as well as throwing in the trademark flicks and tricks that have come to define his game.
PSG is looking to regain the French crown from AS Monaco having enjoyed a reign of four-straight victories before finishing runner-up last season.
Late drama sees Lazio triumph
Elsewhere in Europe, Lazio survived a late scare to beat Juventus 3-2 to claim the Italian Super Cup.
Paulo Dybala scored in the 84th and 91st minutes to draw the Bianconeri level after a brace from Ciro Immobile had given Lazio the advantage.
There was more drama to come, however, as moments before the final whistle, Alessandro Murgia calmly turned in a cross from Jordan Lukaku.
Juventus, Champions League finalist and winner of Serie A for the past six seasons, was chasing an eighth Super Cup title, but substitute Murgia's late, late finish helped Lazio add to victory in last season's Coppa Italia in dramatic style.
"I am struggling to keep a lid on my emotions," said
"I cried at the end of the game, because this team gave absolutely everything and the fans deserved this trophy."