Provincial secretary Thanduxolo Sabela described the 26 ANC Members of Parliament as "suicide bombers".
The motion of no confidence in Zuma was held in Parliament on Tuesday, August 8.
Zuma survived the motion of no confidence in his presidency by 198 votes to 177, with 9 abstentions. The vote was secret.
"Mantashe must institute an investigation on all ANC MPs. We can't just act like we didn't see that there were 26 suicide bombers in the ANC, trying to set alight the house while we were inside," he said.
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Sabela said those ANC MPs "who were clear on voting for Zuma to go" must just face disciplinary action.
"There were those who were clear when they spoke on TV about how they would vote. Dr Makhosi Khoza must be subjected to disciplinary committee. Derek Hanekom was also very clear," said Sabela.
He was speaking at the ANCYL's Economic Freedom Lecture on Land and Minerals at the Durban University of Technology on Saturday.
Sabela "sent a message" to ANC MPs.
"Once it becomes about you and your personal feelings, do the noble thing and leave the ANC seat. Go and represent yourself and family. While you are still in the party seat, you must toe the party line," he said.
He said ANC members who have voted against the ANC before - including those at local and provincial government - had been expelled from the party.
He also called the Speaker of the National Assembly Baleka Mbete to investigate the "influence of money" during Tuesday's motion of no confidence, "on her capacity as a government official.
"We are aware that there was a lot of money spent during the motion of no confidence. The Speaker should investigate all the MPs, not just ANC MPs, because they can't be honourable if they are bought. They are dishonourable," said Sabela.
Once there's a suspicion that there was money involved, it means there must be an investigation, he said.
"The public must be made aware of the outcome of the investigation, that's a government process," he said.