The report released by the Public Protector, a constitutionally-mandated watchdog in November, called for a judicial inquiry into allegations that Zuma, some cabinet members and some state companies acted improperly.
Mkhwebane was speaking during a media briefing held in Pretoria on Monday.
She said this failure constitutes "improper conduct and maladministration" and wants the SIU to recover the "misappropriated" public funds unlawfully given to Absa and investigate other institutions mentioned in the Ciex report.
Madonsela found extensive indications that the Gupta family's business empire has been given allowed to benefit from contracts with state enterprises, notably Eskom.
Mkhwebane said the changes in the final report were made as a result of responses from parties who were implicated in the report - including the treasury, the presidency, the Reserve Bank and Absa.
"I am opposing the review by the President, including the Minister Zwane and Minister van Rooyen's applications because remember, they've also applied for judicial review to set aside the whole report", she further said.
The SIU now has the task of investigating the bailout and recovering public funds paid to Absa. Comrades who were in government when the CIEX report came out where defensive when it came to this matter. Mkhwebane said Absa has paid some of the money back, but not the two decades' worth of interest that has accumulated.
South African bonds weakened on Monday afternoon in line with the rand, which in turn, was affected by local political concerns.
Public Protector Busisiwe Mkhwebane, an anti-graft watchdog, recommended constitutional changes to make the central bank promote economic growth rather than currency and price stability.
Section 224 deals with the primary object of the South African Reserve Bank.