The on-loan Crystal Palace forward gestured towards the visiting fans at Selhurst Park on Saturday after taunts regarding his move to the Premier League leaders
Zaha, who will remain on loan at Palace until the end of the season after agreeing a move to Old Trafford in the January transfer window, smiled and gestured after being taunted by the away supporters.
United and Leeds remain fierce rivals despite the Yorkshire club's relegation from the Premier League in the 2003-04 season.
"On that note I also wanted to apologise for the gesture I did towards the Leeds fans in yesterday's game," Zaha tweeted. "Very unprofessional from me."
Zaha has scored six goals for Palace in the Championship this season and also made his debut for England in the November friendly against Sweden.