Sergio Canales and Carlos Gurpegui both suffered knee ligament damage during the 1-1 draw between Valencia and Athletic Bilbao.
In two completely unrelated incidents, both players were forced off during the match at the Mestalla.
Canales, on loan from Real Madrid, was forced off on the half-hour, whilst Bilbao skipper Gurpegui was substituted just before the hour.
Valencia sent Canales for scans on Sunday, which confirmed that he had torn an anterior cruciate ligament.
Los Che are now in talks with Canales' parent club Real about how to treat the midfielder and who should conduct the surgery, which will take place later this week.
Bilbao confirmed on Monday that an MRI scan had revealed that Gurpegui had also damaged his anterior cruciate, and he too would go under the surgeon's knife this week.
Both players are expected to be sidelined for a minimum of six months.