Zaha had already accepted the charge but requested a personal hearing with the FA's disciplinary panel after he made a gesture towards Leeds fans during the 2-2 draw at Selhurst Park on 9 March.
The ban comes into immediate effect, ruling Zaha out of Palace's home game with Birmingham on 29 March once Championship football resumes after the international break.
Zaha apologised afterwards on Twitter, saying: "I...wanted to apologise for the gesture I did towards the Leeds fans in yesterday's game. Very unprofessional from me."
Eagles manager Ian Holloway had already accepted a charge of improper conduct relating the same game for comments made to match officials after the final whistle.