Asensio suffered the injury in the surprise defeat by Mallorca and, during Tuesday's training session in Morocco, was still feeling discomfort that will lead him to miss the last-four clash.
Manager Carlo Ancelotti also got the news on Wednesday that goalkeeper Thibaut Courtois, who didn't make the trip to Rabat on Monday, will not recover from a groin injury in time to fly out should Real qualify for Saturday's final.
Forwards Karim Benzema and Eden Hazard and defenders Eder Militao, Lucas Vazquez and Ferland Mendy also stayed in Madrid for treatment.
Hazard, Vazquez and Mendy have been out with long-term injuries but Benzema and Militao, who were substituted in the LaLiga win against Valencia last Thursday, are not expected to be sidelined for too long and could join their teammates in Rabat later in the week.
Ancelotti will be crossing his fingers that his key players can return quickly as they follow their trip to Morocco with Champions League last 16 matches against Liverpool and a Copa del Rey semi-final against Barcelona, as well as trying to catch their arch rivals in LaLiga.
Barca are top, eight points ahead of second-placed Real.
The winners of Wednesday's match will face Al-Hilal in the Club World Cup final. The Saudi Arabian side delivered a stunning 3-2 win against South American champions Flamengo in the other semi-final in Tangier on Tuesday.
