In recent weeks, two ANC lawmakers who publicly said they meant to vote against Zuma were quickly censured by the party.
"This decision is therefore in the best interest of the country".
City Press reported on Sunday that opposition parties claimed that they had secured enough votes to meet the 201 "yes" votes they need to remove Zuma.
South Africa's top court had ruled on June 22 that the speaker of the parliament can order a secret ballot for no-confidence motions, an outcome the opposition hopes would embolden ANC MPs to rebel and depose scandal-plagued President Jacob Zuma.
Several high-profile party stalwarts, including the former finance minister whom Zuma fired in March, have publicly called on him to step down. Even more ludicrous is to seek to hide behind disciplinary action which will achieve nothing but serve to avoid the real issues that these comrades and many others are raising.
But the ANC has warned that any of its MPs who support the anti-Zuma no confidence motion risk being disciplined by the party.
The rand rose to 13.1825 on Monday, its firmest since July 31, soon after the parliamentary speaker allowed a secret ballot in the opposition-sponsored vote taking place later on Tuesday. Zuma has survived six earlier no- confidence votes since becoming president in 2009.
"There is no Constitutional obligation for a parliamentary member to swear an oath of obligation to their political party", she said.
After the debate on the motion of no confidence, the National Assembly will be prepared for voting and then the bells will be rung to call MPs back to cast their votes.
Mtehmbu's office reiterated their stance that ANC members will vote against the motion.
ANC members of parliament can never be participants in the demise of their own government and their own organization, Mthembu noted.
The EFF also accused Mbete of deliberately delaying the announcement of her decision so opposition parties would not have insufficient time to legally respond to the decision.
"Having considered all the factors, and mindful of the fact that this decision is not setting a precedent, I determine that voting on the motion of no confidence in the President on 8 August 2017 will be by secret ballot".
She said she has taken due political, legal and Constitutional input in arriving at the decision.
Also Monday, in the city of Durban in Zuma's home province, dozens of traditional and faith leaders gathered to appeal to God to save the president.
"Instead of solving our problems, we would be doing more harm to our country", he added.
The ANC in the Dullah Omar Region applied for 15 000 participants to march from the Grand Parade to Parliament, said City of Cape Town spokesperson Hayley van der Woude.