The Advertising Standards Authority has received more than 200 complaints about the ad from viewers who said it was "offensive", "inappropriate" and "unsuitable to be seen by children".
Heinz decided to withdraw the ad less than two weeks after it first aired, stating that it was listening to its consumers.
Ben Summerskill, the chief executive of Stonewall, said: "We're shocked that an innocuous ad should have been withdrawn in this way. I can't imagine that Heinz would respond to protests about black people featuring in their adverts.
"Our phones have not stopped ringing with supporters who are deeply upset."
The Heinz Deli Mayo ad, created by Abbott Mead Vickers BBDO, showed a family going about their morning routine with mum making sandwiches for the kids' lunch boxes.
However "mum" turns out to be a male uniformed New York deli sandwich maker and before the husband leaves the house, "she" reminds him to give "her" a kiss goodbye.
The two men kiss and the sandwich maker says: "Love you. Straight home from work sweetcheeks."
The idea behind the light-hearted ad is that Heinz Deli Mayo is so authentic that it tastes as though anyone with a bottle has their own New York deli man in the kitchen.
Nigel Dickie, a spokesperson for Heinz, said that the ad was intended as "a humorous take on a slice of life" but that it had decided to pull it because of "consumer feedback". The campaign had been due to run for five weeks.
The ad already has an ex-kids restriction, meaning it cannot be shown in or around children's programming, because Heinz Deli Mayo comes under Ofcom's restrictions relating to products that are high in fat, salt or sugar.
In March, the advertising watchdog refused to uphold 54 complaints about Stonewall's billboard campaign tackling homophobic bullying.
The campaign, which featured the slogan "Some people are gay. Get over it!", received seven complaints that it was "inappropriate for display where it could be seen by children" and five that the ad was "particularly offensive to Christian and other groups".