Protesters from the left-wing Economic Freedom Fighters (EFF) group targeted six shops in Gauteng province, police said.
Video posted on social media showed racks of clothes being pushed to the floor.
In one location, rubber bullets were fired to disperse demonstrators. While officers are monitoring the situation, they said they had not made any arrests so far.
The controversy began when the chain issued an image of a black child modelling a sweatshirt with the slogan “Coolest monkey in the jungle”.
In an apology on its local website, H&M said: “Our position is simple: we have got this wrong and we are deeply sorry.”
The company said it had removed the image from all its marketing.
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But EEF spokesman Mbuyiseni Ndlozi was unimpressed. “The time of apologies for racism are over; there must be consequences to anti-black racism, period!” he tweeted.
Manchester United striker Romelu Lukaku has also hit out at the advert, modifying the slogan to read “Black Is Beautiful”.