The 23-year-old collapsed during the 3-2 loss at Real Union in the Copa del Rey in October.
De la Red is still undergoing tests to determine a definitive diagnosis.
Ruud van Nistelrooy and Mahamadou Diarra will also miss the rest of the season with injuries.
“I can’t remember a situation like the one we are in right now, with three players sidelined for the entire season,” Real president Ramon Calderon told Spanish television station La Sexta.
