Members Lumko Mtimde, John Danana, Cedric Gina, Desmond Golding, Cawe Mahlati and Noluthando Gosa tendered their resignations on Monday.
Last week, SABC board chairperson Ben Ngubane and his deputy Thami ka Plaatjie resigned following weeks of renewed tension at the public broadcaster after Ngubane and the board fell out over the future of acting chief operating officer Hlaudi Motsoeneng.
On February 26, the broadcaster announced Motsoeneng had been "released from his duties". It said that Mike Siluma, a veteran journalist and head of radio news and current affairs, had been appointed to the acting position.
But shortly after that, Ngubane was quoted in a newspaper report as saying Motsoeneng had been reinstated. He said Ka Plaatjie had made this decision.
This prompted the SABC board to issue a media statement saying that "the report … is regrettable as neither the chairperson nor the deputy chairperson nor both have the power or authority to unilaterally change a board resolution".
The SABC board said it would seek clarity from Ngubane and Ka Plaatjie regarding the newspaper report. Since then, Pule has asked Parliament to "urgently" review the fitness of the SABC board.
Communications Minister Dina Pule tried to persuade the pair to withdraw their resignations but Zuma has, in the meantime, accepted and thanked them for their tenure at the SABC.
Pule will now have the tough job of filling the vacancies.