Zuma is arguing that he was not given enough time to respond to questions posed to him by former ombudswoman Thuli Madonsela during the investigation into "state capture" by the Gupta family.
The report investigated allegations that Zuma allowed the Gupta family undue political sway, including letting them choose some cabinet ministers.
Four opposition parties are challenging Zuma's bid in a case heard in the High Court in Pretoria.
Madonsela concluded the report last month, shortly after the expiry of her seven-year non-renewable term.
The report was due to be released on October 14 but Zuma moved to block it.
The application to halt its release is also backed by Local Government Minister David van Rooyen and Mines Minister Mosebenzi Zwane, who too are named in the report.
Dali Mpofu, the lawyer representing the opposition parties, said Zuma's application was motivated by fears that his implication "might lead to the invocation of the impeachment proceedings or motion of no confidence."
Deputy finance minister Mcebisi Jonas early this year accused the family of offering him the job of finance minister, something he said he rejected.
Zuma, 74, has survived a string of damaging scandals, but has faced increasing criticism as the economy has stalled and after the ruling ANC party suffered unprecedented losses in local polls.
Earlier this year several banks and audit firms in South Africa cut ties with Gupta-owned firms.
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