"The implications of this are that black identity exists as inferior to the identity of white people. It is an assertion that white standards of beauty are to be aspired to and features of black represent damage, decay and abnormality," the EFF said in a statement.
The party members, who often dress in red overalls as a show of solidarity with workers, held similar protests in 2018 against clothing retailer H&M after the company published a catalogue in which a black boy wore a hoodie bearing the slogan "coolest monkey in the jungle".
The EFF, formed in 2013 by Mr Malema, has always taken a populist approach to distinguish itself from the ruling African National Congress (ANC) which it accuses of straying from its revolutionary ideals.
Mr Malema has charged that the ANC has neglected the poor - mostly black - community and instead represents the interests of big businesses, which are largely controlled by the white minority.
Many say racism remains embedded in South African society, 29 years after the end of apartheid.
The Clicks advert, which has since been withdrawn, was posted online last week.
"[I am] deeply disappointed that we allowed insensitive and offensive images to be published on our website," Clicks boss Vikesh Ramsunder said in a statement on Sunday.
He added that the "negligent employees" had been suspended.
His apology has not assuaged EFF supporters who raided several stores across the country on Monday.
on Twitter show some Clicks stores closed, while others have security guards forming a protective line in front of singing protesters.
In another video
the party supporters are seen pulling down shelves in a store.
In Mpumalanga province, a group of people threw a petrol-bomb at a Clicks store in Emalahleni municipality.
"According to information that we have gathered, around 1am a group of men came and threw a petrol bomb at the shop. However, only a few glass [panes] were cracked but the shop itself is safe, nothing was damaged in the shop," said the province's police spokesperson Leonard Hlathi.