Los Blancos took the lead in the 13th minute of the contest at Estadi Mallorca Son Moix, but Vedat Muriqi levelled the scores early in the second period, and Carlo Ancelotti's side could not find a second.
Real Madrid were reduced to 10 men in the latter stages of the contest when Mendy brought Muriqi to the ground with a poor challenge, with referee Cesar Soto Grado quick to produce the red card.
There had been suggestions that the France international could be in line for an extended ban due to the nature of the challenge, but it has now been confirmed that he will miss just the one match.
Mendy will serve a one-game ban for Real Madrid
"The Disciplinary Committee of the Spanish Football Federation (RFEF) has imposed a one-match ban on Real Madrid player Ferland Mendy, following his expulsion due to a direct red card in the first round of La Liga match against Mallorca," read a statement from the RFEF.
As a result, Mendy will be absent for Sunday's La Liga clash against Real Valladolid, but he will be available again to take on Las Palmas on August 29.
There had been some speculation over the 29-year-old's future earlier this summer, with Real Madrid seemingly pushing to sign Alphonso Davies from Bayern Munich.
However, Mendy will be staying with Real Madrid this season and is again expected to be the first-choice left-back, having impressed for Ancelotti's side during the 2023-24 campaign.
Mendy will sit out the game with Real Valladolid alongside injured duo David Alaba and Eduardo Camavinga, but the Spanish and European champions did not pick up any fresh fitness problems in their first game of the new campaign.
Who will feature at left-back in Mendy's absence?
Fran Garcia is in line to start against Real Valladolid, with the 25-year-old set to feature alongside Dani Carvajal, Eder Militao and Antonio Rudiger at the back this weekend.
Garcia secured a return to Bernabeu from Rayo Vallecano last summer, and he made 31 appearances in all competitions during the 2023-24 season, including 25 outings in La Liga.
Ancelotti could make just the one change to the side that started against Mallorca, with Rodrygo, Kylian Mbappe, Vinicius Junior and Jude Bellingham again all set to start.