Real are due to face city rivals Atletico Madrid for the right to lift the Spanish Cup.
They will go into battle without the services of the versatile Varane, as the Frenchman has suffered a setback that will require surgery.
He fell awkwardly during Saturday's 1-1 draw with Espanyol and was forced from the field just 19 minutes into that contest.
"The tests today have revealed an injury to the meniscus. They are going to operate on me as soon as possible," Varane posted on his Twitter account on Tuesday.
The 20-year-old has been a standout performer during a difficult season for Real, but coach Jose Mourinho believes he has quality cover at his disposal.
He said: "We have alternatives. It's a position where we have people who are playing, and who are fit.
"Obviously, we are sad that he could miss a game everyone would want to play in, but we aren't going to over-dramatise because we have options in that position."