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 one instance, officers fired rubber bullets to disperse the protesters, the police added.
H&M earlier this week issued an apology for the widely criticised ad, which featured a black child modelling a sweatshirt with the slogan "coolest monkey in the jungle", and said it had removed it from all its marketing.
"The time of apologies for racism are over; there must be consequences to anti-black racism, period!" Ndlozi wrote on Twitter, posting pictures of a vandalised H&M store and video footage of chanting EFF supporters.
H&M South Africa did not respond to a request for comment, but its local website carried an apology for the advertisement.
"Our position is simple, we have got this wrong and we are deeply sorry," the apology read.
Police said they were monitoring the protests, but that they had made no arrests so far.
Protests over perceived corporate wrongdoing have a history of turning violent in South Africa, where some drivers for ride-hailing service Uber have had their vehicles torched over the past year by regular taxi operators.
(Reporting by Alexander Winning; editing by Alexander Smith)
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