COSATU has always been the president's staunch ally and stood by him when Zuma was reelected for another five years in 2014.
President Jacob Zuma sacked Finance Minister Pravin Gordhan because their relationship had irretrievably broken down, the African National Congress (ANC) said on Wednesday.
Cosatu, which was instrumental in Zuma's rise to the presidency in 2009, said in a statement that it was time for a new collective to lead at government level.
Opposition parties brought the motion after Zuma's abrupt recall of former finance minister Pravin Gordhan from an investor roadshow overseas, which preceded his midnight Cabinet reshuffle last week.
Three of the ANC's top officials - deputy president Cyril Ramaphosa, secretary general Gwede Mantashe, and treasurer general Zweli Mkhize - have accepted that they made a "mistake" by publicly criticising President Jacob Zuma following his Cabinet reshuffle.
Cosatu general secretary Bheki Ntshalintshali said the federation had its doubts over Zuma's leadership abilities.
Mantashe accused the media of attempting to convince ANC cadres to vote with the opposition to remove President Zuma.
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Jonas was at the center of the state capture scandal after revealing that he was approached by friends of the president, the Gupta family, with an offer to be finance minister - on condition that he assist them in securing billions of rands' worth of government contracts.
Opposition parties, together with some in his own governing alliance, are planning mass action through public protests and are still demanding for him to resign.
S&P said the cut to below investment grade reflected "heightened political and institutional uncertainties" following Zuma's shock purge of critical ministers.
Newsmen report that on March 30, Leader of a South African opposition party, Julius Malema, filed for disciplinary or impeachment proceedings against Zuma in a court application.
Gordhan's dismissal - and replacement by a Zuma loyalist - led the ratings agency Standard & Poor's to downgrade South Africa's government debt to junk status.
Zuma defended the cabinet reshuffle, saying the reshuffle will add renewed energy into cabinet and the executive as a whole.
Analysts said that despite calls to resign from voices outside the ANC, Zuma remains in favor among grassroots members and can count on the backing of large sections of the party, including the youth and women's leagues.