The motion was filed by the African Transformation Movement (ATM) leader Vuyolwethu Zungula in February, before the COVID-19 lockdown began.
It is linked to the allegations that Ramaphosa misled Parliament about donations made to his CR17 campaign for the position of African National Congress (ANC) president.
National Assembly Speaker Thandi Modise has since declined that the motion be conducted through a secret ballot.
The Democratic Alliance (DA) has already made it clear that it will not support the motion which some political analysts say is not likely to succeed.
The ANC says it is not worried about the motion.
The ATM, however, says they have garnered a lot of support from other parties and they have confidence their motion will pass.