Heinz withdrew the ad for its Deli Mayo brand, which features two men kissing, after the Advertising Standards Agency received more than 200 complaints.
The motion has been signed by five other Labour MPs, and says Heinz's decision is likely to offend millions of gay and lesbian people.
Diane Abbott told Campaign: "I think that Heinz totally misjudged this. I cannot find anyone who was offended by the ad, which was clearly intended as a joke.
"But I have spoke to lots of people - and not just gay and lesbian people - who think that the way Heinz pulled the ad was silly and offensive."
The text of the motion says: "Millions of children watch depictions of same-sex relationships in soap operas every day."
It continues that the ad was "not intended to be a realistic depiction of a same-sex relationship, and that the ad was intended to be humorous".
The original ad was created by Abbott Mead Vickers BBDO.
It was due to air for four weeks, but Heinz's move to drop the ad led gay rights group Stonewall to call for a boycott of Heinz products.
Heinz and AMV BBDO are refusing to comment on the furore.