Zuma and Malema broke ties despite the latter's role in propelling him to power in 2009.
Malema was instrumental in the president's election and campaigned across the nation on his behalf.
Polokwane, which is north of Johannesburg, is the capital of Malema's native Limpopo province.
Malema, once a major ally of the president, is now one of his fiercest critics.
However if Mr Zuma wins this battle, then Mr Malema may fade into political oblivion.
I've read Fiona Forde's new book on Julius Malema but was left wanting much more.
Its leader Julius Malema's signature policy is his demand to nationalize the country's mines.
Mr Malema is also being investigated by state agencies on charges related to corruption and tax evasion.
Then there's the ANC's own Julius Malema - hardly a Cicero but an undisputed master of the punchy soundbite.
Malema and the ANC Youth League helped propel Zuma to power in 2009.
Unfortunately, the celebrations will be overshadowed by the struggle between President Jacob Zuma and his one-time protege, Julius Malema.
Malema has also called for nationwide strikes in the mining industry, dismaying politicians trying to quell labor discontent among workers.
The following year, a court ruled that the song amounted to hate speech - a decision that Mr Malema rejected.
How good, then, to be told by Mr Malema that they are in no way to blame for their plight.
ECONOMIST: The black man who is rude about whites is doing rather well
Mr Malema, 30, wants Mr Zuma replaced as party leader ahead of the 2014 elections and replaced with deputy leader Kgalema Motlanthe.
But Mr Malema's relationship with Mr Zuma has soured in recent years.
If he fails and Mr Malema emerges victorious, that will be the end of Mr Zuma's authority both within and without the ANC.
Mr Malema's Youth League, who helped Mr Zuma come to power, are keen to deprive him of the second term he desperately wants.
Such statements are particularly sensitive because of South Africa's apartheid history and there have been concerns that some would act on Mr Malema's statements.
After months of legal and political wrangling, the ANC disciplinary committee finally suspended Mr Malema for five years for bringing the ANC into disrepute.
Mr Malema's latest rendition has raised the question of whether his right to free speech should be trumped by the constitution's ban on spreading hatred.
Malema's brash, populist message resonates with some of the nation's disenfranchised, who took to the streets in protest when he was ousted from the ruling party.
Malema's controversial road to fame includes his calls to seize white-owned farms in South Africa, especially incendiary in a nation with a history of racial tensions.
Malema was expelled from South Africa's ruling African National Congress this year in the wake of a speech he made that was critical of President Jacob Zuma.
Mr Malema has 14 days to appeal, but was already suspended for his statements on Zimbabwe and so must vacate his position as youth league leader immediately.
In November 2011, a man seen as a potential serious challenger for Mr Zuma's post, the firebrand ANC youth leader Julius Malema, was suspended from the governing party.
Some analysts believe that by acting against Mr Malema, Mr Zuma believed that he was removing a key opponent as he seeks re-election as ANC leader in December.
Most recently, President Jacob Zuma has struggled to control the ANC's militant Youth League leader, Julius Malema, who plays to the gallery of poor and marginalized black South Africans.
Mr Malema has also been forced to defend himself from accusations of making millions from state contracts for firms with which he was involved in his home province, Limpopo.
Mr Zuma was in exile for 30 years and is a much more experienced political player than the 30-year-old Mr Malema: The president is determined to show Mr Malema who is boss.
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