Several hundred protesters marched to the Constitutional Court in Johannesburg in the latest demonstrations against Zuma, who has been implicated in a series of corruption scandals.
Opposition parties have lobbied for a secret ballot and called for African National Congress (ANC) lawmakers to "vote with their conscience".
The ANC holds a large majority in parliament and Zuma has survived similar votes in the past, which have not been secret.
Zuma's sacking of respected finance minister Pravin Gordhan in March has fanned years of public anger over government corruption scandals, record unemployment and slowing economic growth.
Also Read
"Zuma's time is up," 22-year-old marcher Tsido Molefe told AFP.
"We are going to march until he leaves, and today we are here to support the court case," she said.
The president has recently faced unprecedented criticism from senior ANC figures, including from Deputy President Cyril Ramaphosa.
He is seen as favouring his ex-wife, former African Union chief Nkosazana Dlamini-Zuma, to succeed him -- rather than Ramaphosa.
Zuma has been accused of being in the sway of the wealthy Gupta business family, allegedly granting them influence over government appointments, contracts and state-owned businesses.
The dismissal of Gordhan saw the Fitch ratings agency as well as Standard and Poor's cut South Africa's sovereign credit rating to junk status due to fears of political instability and growing corruption.
Disclaimer: No Business Standard Journalist was involved in creation of this content