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The Eoin Morgan-led England are due to fly from London to Cape Town on Monday but will not be travelling if the hosts board and the government are unable to sort out the administrative mess in CSA.
Yacoob, a former Constitutional Court judge, was appointed by Mthethwa to lead the proposed interim board on October 30.
In a strongly worded letter after the CSA Members Council decision, Mthetwha wrote, "I find it most regrettable that you have purported to take the decision not to recognise the Interim Board."
"I implore you and the Members' Council to re-visit this decision immediately, and to afford the necessary recognition to the Interim Board, failing which, I will exercise my powers under the Act and issue a directive in that regard," the minister had written in the letter addressed to CSA's acting president Rihan Richards.
Former CEO Haroon Lorgat, who had stepped down in 2017 after a rift with board members following the failure to launch the now-defunct Global T20 League, was named in the interim board, something which the Members Council didn't approve of.
Lorgat was still the CEO in 2016-2017, a period which has been covered by the Fundudzi report, which was commissioned earlier this year to probe poor governance in CSA.
Reasons behind failure of Global T20 league also forms part of the investigation, the report of which was used to fire Lorgat's successor Thabang Moroe for financial misconduct.
Mthethwa, however, assured that Lorgat would recuse himself from all discussions relating to the Global T20 League.