Police spokesperson, Colonel Lungelo Dlamini, said protestors had managed to gain entrance to the H&M shop in the East Rand Mall and steal several items.
The picture depicted a black child modelling a green sweater bearing the phrase "coolest monkey in the jungle".
"We can't accept that H&M, after what they have done, is coming now and saying we apologise".
The Economic Freedom Fighters (EFF) protesters targeted six H&M stores in the Gauteng province, where South Africa's economic hub of Johannesburg is located, tearing down shop displays and throwing clothes around, police said. In Cape Town, the store manager read the retailer's statement to irate protesters.
Police were called to H&M stores following reports of violence and damage.
According to local media, similar protests were also seen in other shopping centers nationwide.
National Basketball Association star LeBron James, rapper Diddy and singer The Weeknd are among the celebrities who expressed shock in recent days over the H&M image, which has been removed.
"We have a responsibility to be aware of and attuned to all racial and cultural sensitivities - and we have not lived up to this responsibility this time".
But many have already pledged to boycott the store, as The Weekend - a Canadian R'n'B star who produced menswear collections with the chain - said he was cutting ties with the company.
H&M said on Tuesday that it was "deeply sorry that the picture was taken" and promptly removed both the ad and the product.
H&M said procedures had not been followed properly and the company would thoroughly investigate why the incident happened.
The ad, which has been deleted, met backlash earlier in the week when it was shared on social media. "Get over it", Terry Mango wrote in a since-deleted Facebook post.