The winger is understood to have sustained the injury in the first half of the English Premier League tie but stayed on for the entire duration of the clash.
The Guardian reports that the 25-year-old was sent for a scan on Monday to know the extent of the injury, but has been referred for more treatment.
This comes as a huge blow to manager Roy Hodgson who has key members of the first team Scott Dann, Jason Puncheon, Jeffrey Schlupp, Connor Wickham and Reuben Loftus-Cheek all out on long-term injuries. Goalkeeper Julian Speroni and right-back Martin Kelly were, according to the manager, also due to be assessed for knee and hamstring injuries on Monday.
Mali international Bakary Sako - who also is the team's top scorer - was ruled out of the season last week, now leaving Christian Benteke, Andros Townsend and January signing Alexander Sorloth as their only attacking options.
Zaha who was instrumental in turning the Eagles' season around has contributed four goals and several match-winning displays to lift the Selhurst Park outfit out of the relegation zone.
Palace are now placed 14th spot in the top-flight log with 27 points from 26 games.