Jonas had meant to stay on at Parliament but realised after yesterday's briefing from the ANC's national working committee that the party will not allow its MPs to vote with their conscience on April 18.
Demonstrators protest against South African President Jacob Zuma in Pretoria, South Africa, on Tuesday, April 4, 2017.
According to COSATU secretary-general Bheki Ntshalintshali, the unions no longer believe in Zuma's leadership capacity.
Zuma echoed this notion and said the reshuffle was intended "to bring about radical socioeconomic transformation and to ensure that the promise of a better life for the poor and the working class becomes a reality".
Sizwe Pamla, the union's spokesman, said the meeting will discuss the cabinet reshuffle that has cost the country one investment-grade rating and deepened a rift within the ANC.
Rating agency Moody's has said it is reviewing the Baa2 credit rating it assigns South Africa, two notches above junk, a process that could take 30 to 90 days.
In an address on Wednesday just before he resigned Jonas bemoaned the national obsession with who was in power over strengthening South Africa's institutions.
"That public dissonance was a mistake that will not happen again", the party's secretary-general, Gwede Mantashe, said at a news conference after a meeting of the party's leaders.
He is due to step down as head of the ANC in December, ahead of the 2019 general election.
Former high commissioners, ministers and many respected anti-apartheid activists also told the media that the ANC should do "the honorable thing and recall the president", especially after the party's integrity commission advised that he should resign.
ANC spokesperson Nonceba Mhlauli says they have been inundated with mischievous calls, text messages and emails by faceless individuals and organisations lobbying them to disregard the party line and vote in accordance with their individual taste.
Insiders who attended the meeting, which lasted several hours on Tuesday night, said the trio were "lambasted" for speaking out.
Cosatu is the second biggest ANC ally to call on Zuma to quit after South Africa's Communist Party urged him to step down last Friday.
Mr Gordhan was dropped as part of a major cabinet reshuffle which left some in the ANC leadership questioning whether Mr Zuma should remain as president.