"The national executive committee chose to recall the president in accordance with rule 12.2 of the ANC, which allows the ANC to recall it's deployees", Magashule told reporters at the ruling party's headquarters, Luthuli House.
If Mr Zuma, 75, still does not budge, he will face a vote of confidence in parliament that he is expected to lose.
"The decision by the NEC to recall its deployee was taken only after exhaustive discussion on the impact such a recall would have on the country".
The Presidency had initially planned to hold a media briefing for President Jacob Zuma at the Union Building at 10:00 on Wednesday, but the request was later withdrawn, an official email shows.
Opposition parties are calling for another vote of no confidence against Zuma next week.
Magashule said the party did not give Zuma a deadline to tender his resignation, but said they expected a quick turnaround.
Zuma retains significant support inside the party and at a local level in many parts of South Africa.
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Mr Zuma has resisted increasing pressure to quit since December, when Cyril Ramaphosa replaced him as leader of the ANC.
"Zuma told Ramaphosa and Magashule that he would respond to them publicly when the party informed him of the decision to recall him", a source said.
Citing unidentified ANC sources, South African media say Zuma has asked for state security for his family, payment of legal fees and a few more months in office.
The impasse has plunged South Africa - the continent's most developed economy - into confusion over who is running the country, with major national events cancelled amid the uncertainty. If Zuma digs in and refuses to be fired, he has to be removed through a parliamentary motion.
In 2008, Zuma's supporters pushed out then-president Thabo Mbeki via a similar "recall" over allegations of abuse of power.
Besides his controversial relationship with the Guptas, who were born in India but moved to South Africa in the early 1990s, Zuma has 783 counts of corruption outstanding against him relating to a 2.5 billion dollars state arms deal in the late 1990s.
A judicial commission could soon begin to examine allegations of influence peddling and illegal contracts to Zuma cronies.
The President's term had been due to end next year.