It has been withdrawn following accusations of racism.
Reports indicated that the H&M shop at Sandton City in Johannesburg had been trashed on Saturday.
Video footage of the protests showing members of the EFF destroying H&M's property has surfaced on social media.
Earlier in the week, H&M said: "We understand that many people are upset about the image".
US President Donald Trump has also been criticized for allegedly describing African nations and Haiti as "shithole countries".
H&M released a statement on their Twitter page, announcing that stores around the area have been closed for the safety of their employees and customers.
EFF commander-in-chief Julius Malema made no apology for his fighters' conduct on Saturday, saying their actions should have taught the massive worldwide retailer a lesson.
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"Every shop that undermines black people must be attended to", Malema added.
Gauteng police spokesperson Lieutenant Colonel Lungelo Dlamini said the police were now investigating cases of malicious damage to property and illegal gathering.
The police haven't arrested anyone so far. Ndlozi wrote on his Twitter.
The racism scandal has hit the Swedish company at a time when it is struggling to make the switch to e-commerce, analysts say.
"We continue to monitor the situation closely and will open the stores as soon as the situation is safe again".
H&M South Africa did not respond to a request for comment, but its local website carried an apology for the advertisement.
She went on to slam the incident but later shaded the DA for claiming that the EFF should be made to pay for the damage caused.
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.