Unless he resigns beforehand, parliament will hold a vote of no-confidence in the president on Thursday, when the ANC says its lawmakers will finally oust him from power.
Ace Magashule, secretary-general of the African National Congress, says the party's national executive committee has chose to "recall" Zuma.
The African National Congress has tried for weeks to get Zuma, whose term expires next year, to resign and cede the country's leadership either to Deputy President Cyril Ramaphosa, who was selected in December to replace Zuma as head of the party, or to a caretaker president.
Should Zuma fail to obey the ANC's call for him to step down, Gigaba warned that the party would use the vote of no confidence in parliament to remove him from the Union Buildings.
"We don't want to keep South Africa waiting".
"Zuma has been unloved by the markets and we are likely going to see the rand firm", Mpofu said, referring to the country's local currency.
The drop in the party's public support during Zuma's rule - the ANC lost control of Johannesburg, the economic hub, and Pretoria in municipal elections in 2016 - ironically gives him leverage. Reuters news agency said Zuma's spokesman could not be immediately reached for comment.More news: Brooklyn judge blocks Trump admin from ending DACA
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South Africa's cabinet meeting set for Wednesday has been postponed indefinitely, the government's communication service said.
In 2008, Zuma's supporters pushed out then-president Thabo Mbeki via a similar "recall" manoeuvre over allegations of abuse of power.
But Magashule, during the media briefing at Luthuli House, said that it would be expected that Zuma would respond today.
Magashule's explanation on the reasons for Zuma's dismissal skirted the scandal that has dogged his presidency, stating only that the decision was procedural - the desire to ensure that the incoming president lead the party into elections next year.
Despite the damning decision to order Zuma's "recall" - party speak for "removal from office" - domestic media said the 75-year-old might yet defy the party's wishes.
The labour federation's general secretary, Bheki Ntshalintshali, said on Wednesday that the threats mentioned by Zuma in an interview with the SABC would not materialise.
Besides his controversial relationship with the influential Guptas family, Zuma has 783 counts of corruption outstanding against him relating to a multi-billion dollar state arms deal in the late 1990s. Opposition parties are calling for another vote of no confidence against Zuma next week.
Zuma became South Africa's fourth president when he assumed office in May 2009.