Ramaphosa also wants any possible impeachment process to be blocked, saying in his 59-page application that "any steps taken by the National Assembly pursuant to the report are equally unlawful and invalid."
The inquiry relates to findings that large sums of foreign currency were hidden at Ramaphosa's private game farm and he failed to report the money missing when it was stolen in 2020.
Ramaphosa has denied wrongdoing and has not been charged with any crimes. The existence of the cash at the Phala Phala game farm and his failure to report the theft to police only surfaced in June in a scandal dubbed "Farmgate" by the media.
Ramaphosa insisted at the weekend that he would not resign after a special panel reported on an alleged coverup of a cash robbery at his farm, but his political future remains uncertain.
The speaker of the National Assembly said on Monday that a closely awaited parliamentary vote that may result in Ramaphosa's impeachment has been postponed by one week.
"We all agree to the 13th (of December)," Nosiviwe Noluthando Mapisa-Nqakula said during a late-night urgent meeting of the parliament's programming committee.
To succeed, the vote would have to be approved by a two-thirds majority of the National Assembly.
South Africa's ruling party on Monday warned it would not back any motion at an upcoming parliamentary debate that would lead to a vote for removing President Cyril Ramaphosa, under fire over a burglary scandal.
The African National Congress interim secretary-general Paul Mashatile said earlier should parliament proceed "the ANC will not support that vote."
Having received firm backing from his allies within the party, Ramaphosa has vowed to fight on, with his spokesman saying the allegations against him would be challenged.
Despite the doubts raised over Ramaphosa's integrity, he is still seen by investors at home and abroad as cleaner than any of his rivals.
Investors fear uncertainty and that any other president could slow down or reverse economic reforms and increase government spending and take on more debt at levels they deem unsustainable.
"The conundrum for the ANC is that recent polls of its supporters show that President Ramaphosa remains its strongest drawcard for national elections," JP Morgan analysts said in a note to clients.
South Africa’s main opposition liberal Democratic Alliance (DA) party said it had submitted a motion to dissolve the national assembly and reiterated its call for an early election.
"Parliament’s role is precisely to step up at times such as this... It can only do this by dissolving the National Assembly so that the president can call an early election," said DA leader John Steenhuisen.
This report was compiled using data from Reuters and Agence France-Presse.