The Championship club revealed on their website that 20-year-old Zaha has also been fined £3,000 for the incident which happened during the 2-2 draw between the sides on March 9.
Zaha, who in January agreed a move to Leeds' historic rivals Manchester United, was photographed appearing to raise his middle finger towards the away supporters.
He 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."
Zaha attended a personal hearing on Tuesday and was handed the suspension which will keep him out of next Friday's home game against Birmingham.
Palace boss Ian Holloway accepted a charge of misconduct towards the match officials following the same game and was last week fined £2,000.