The retailer, which has five stores in South Yorkshire, faced criticism online from people accusing it of being inappropriate, disgusting and negligent.
The image of the model wearing the green monkey hoodie has been removed from its website, while two others featuring different designs in the same category and modelled by white children remain.
Referring to the green top, Labour MP Kate Osamor tweeted: "I was totally shocked, dismayed to say the very least to find this online imagine. H&M do you think this imagery is an appropriate representation of a young black boy?"
Alex Medina, who works in brand design, said it was negligent to place a black child in a top with such a slogan, while white children wore others.
He tweeted: "In the year 2018 there's no way brands or art directors can be this negligent and lack awareness.
"We have to do better."
A person tweeting under the handle @vulkaanrots said they would boycott the store.
They said: "This is beyond disgusting."
A spokeswoman for the retailer said: "This image has now been removed from all H&M channels and we apologise to anyone this may have offended."