Mbete, the speaker of parliament, made a surprise decision Monday to hold the ballot in secret after a campaign by the opposition who hoped to encourage ANC members to vote against their leader without fear of intimidation.
Zuma, 75, is due to step down as head of the ANC in December, and as president before the 2019 general election — lessening pressure for his party to trigger imminent change.
The ANC has acknowledged recent criticism of the party, including the impact of a cabinet reshuffle in March when respected finance minister Pravin Gordhan was replaced with a close Zuma ally.
Gordhan's sacking led to a string of downgrades to South Africa's credit rating as well as causing the rand currency to tumble.
Public support for the ANC, which swept to power under Mandela in the first non-racial elections in 1994, slipped to 55 percent in last year's local polls — its worst-ever result.
A handful of MPs, including Gordhan, have publicly joined calls from anti-apartheid veterans and trade unions for Zuma to resign, as South Africa endures record unemployment and a recession.
Zuma has been engulfed by corruption allegations while in office.
A court last year found him guilty of violating the constitution after he refused to repay taxpayers' money used to refurbish his private rural house.
He has been accused of being in the sway of the Gupta business family, allegedly granting them influence over government appointments, contracts and state-owned businesses.
He is also fighting a court order that could reinstate almost 800 corruption charges against him over a multi-billion dollar arms deal in the 1990s.
Zuma is seen as favouring his ex-wife, former African Union chief Nkosazana Dlamini-Zuma, to succeed him ahead of Deputy President Cyril Ramaphosa.