The winger picked up an injury while on international duty this week.
Per his national team coach Patrice Beaumelle, Zaha has a grade one or two hamstring strain.
Zaha could miss his side's FA Cup semi-final against Chelsea.
"After the first game [against France], he felt some pain behind in the hamstring," said Beaumelle.
"We don't have to take any risks because if it gets worse it is maybe six weeks or two months out. Imagine we put him in and after five minutes…for what? And it was an opportunity for other players to play as a team, but of course I would have liked him to play with the Elephants."