ANC secretary general Ace Magashule said South Africa's ruling party wants an "amicable solution" after calling on Zuma to step down.
Mr Zuma has been under pressure to stand down since Mr Ramaphosa, a union leader and lawyer once tipped as Mr Mandela's choice to take over the reins, was elected as head of the 106-year-old ANC in December. If he doesn't resign, a vote of no confidence has been scheduled in parliament for February 22, which could lead to Zuma's removal from office.
Ramaphosa has held private talks with the president on a power transition, angering opposition parties who described the process as an affront to South African democracy.
"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.
Two other suspects are expected to hand themselves in, the police said.
Wednesday's cabinet meeting, usually chaired by Mr. Zuma, has been postponed because of "developments taking place in the ruling party", a government statement said.
Ramaphosa narrowly defeated Zuma's ex-wife and preferred successor, Nkosazana Dlamini-Zuma, in the leadership vote, forcing him to tread carefully in handling Zuma for fear of deepening rifts in the party a year ahead of an election. The ANC chairperson is also on record to have said if Zuma failed to respect the recall they will employ more drastic means.
But many South Africans, exhausted of Zuma's scandal and corruption tainted leadership, want him to step aside now.
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"President Zuma has since been treated as a scapegoat", Seepe said.
Magashule said he went with deputy secretary general Jessie Duarte to inform Zuma about the decision on Tuesday morning.
"We call all our members and supporters to remain calm and afford the ANC NEC space to handle this matter to its finality in the best interest of the country and the organisation", she said.
"Is it not short-sighted of the ANC not to give President Zuma a deadline to resign?"
Although Magashule and Ramaphosa have both spoken of the need to preserve Zuma's dignity and to avoid humiliating him, the spectacle of a party dislodging a man determined to stay on has been anything but dignified.
Zuma, who took office in 2009 and is in his second five-year term, has not made any public appearances in recent days.
Ramaphosa, the deputy president, must revive the economy and crack down on what he has admitted is rampant government corruption if he is to boost the party's tarnished reputation before a tricky election next year.
South Africa has busted into the property of Gupta family amid an inquiry to look into what's recognized as state capture.