The 25-year-old has reportedly returned to London to undergo medical assessments as the 'Eagles' take on Everton in the Premier League on Sunday.
However, Palace refused to confirm whether the problem is a groin injury, insisting all players returning from international duty will undergo tests.
Zaha registered an assist in Ivory Coast's 4-0 win over the Central African Republic on Friday, who they face in a return match on Tuesday.
If Zaha is sidelined for Sunday's game, Roy Hodgson faces a selection headache with Christian Benteke ruled out until January with a knee injury.