The ad would have been aired on SABC on Monday night until February but it was pulled just two hours before it was scheduled to be flighted, The Star reported.
The animated commercial begins with the words "Dinner time at Nkandla" appearing over a picture of a mansion.
The next frame is indoors. A woman, seated at one end of an extremely long dining room table lined with children and several other women on both sides, says in isiZulu: "Oh Zuzulicious, we're having fish and chips from Shabba today."
The huge family enjoys the fish and chips dinner.
An animated Zuma responds: "Eat up honeybunch, there is a lot of good food here. It's from the Fish and Chip Company. There are many of you in this house, at only R25 even Pravin will approve this."
Paul Warner, the creative director at MetropolitanRepublic Group, the agency that made the ad, said they were told the commercial was banned because it was "degrading to the president".
"They said our [SABC] bosses have made the decision not to flight it," he was quoted saying.
Warner reportedly told the newspaper that there was nothing wrong with the ad, he did not understand how it could be pulled on the basis of being offensive without anyone complaining about it.
Carlo Gonzaga, the chief executive of Taste Holding, under which the company falls, said it was "astounding" that the SABC would take a unilateral decision on behalf of the public. "I think it's presumptuous."
SABC spokesperson Kaizer Kganyago said he was not aware of the ad or any official issuing instructions for a commercial not to be aired.