Los Blancos won their first two games of the summer, up against local rivals Alcorcon and Leganes, ahead of incoming August clashes with Fiorentina, Ferencvaros and Deportivo.
Those matches build towards a LaLiga return for Mourinho on August 22 - away at Espanyol - and his team will now also take on Bundesliga side Schalke 04 on August 16.
That does not impact Real Madrid's own start to the league season, but it will be played after the first game takes place elsewhere in the Spanish top-flight, which restarts on August 15.
The main reason for the club's decision focuses on Mourinho's concern over several key stars only playing limited games in preseason due to extended summer breaks following the 2026 FIFA World Cup.
Marc Cucurella, Jude Bellingham and Real Madrid's French contingent are all still away after a run to the semi finals and final of the tournament.