The pair are suffering from calf muscle injuries and were left out of the 23-player squad travelling to Saudi Arabia for the competition.
The club said the injuries were still being assessed, but Spanish sports daily AS estimated they could be out of action for up to a month.
Both players started on Saturday as Real lost 2-1 at Villarreal during the 16th day of La Liga. World Cup finalist Tchouameni was replaced after an hour but Alaba played the entire game.
Real, the Spanish and European champions, face Valencia, the losers in last season's Spanish cup final, on Wednesday evening in Riyadh.
On Tuesday, Real will prepare for the game at the training ground of Al Nassr, the club that is now home to their former star Cristiano Ronaldo.
In the other semifinal, Spanish cup winners Betis face Barcelona.
The final is scheduled for Sunday.