She probed allegations that he let the wealthy Gupta family wield undue political influence in his government. They have denied any wrongdoing.
Mr Zuma said the report was unlawful as he had not been given a proper chance to respond to the allegations.
Meanwhile, the Nelson Mandela Foundation has called for his sacking.
In a hard-hitting statement, the foundation said Mr Zuma had “failed the test” of leadership and South Africa’s democracy as under “a real threat”.
It supported efforts to hold to account those responsible for “compromising our democratic state and looting its resources”, said the foundation, which is run by close colleagues of South Africa’s first black president who died in 2013.
Mr Zuma has been dogged by allegations of corruption for more than a decade.
He was sacked as deputy president in 2005 after his former financial adviser, Schabir Shaik, was convicted of corruption.
But four years later Mr Zuma was elected president in what was regarded as one of most remarkable political comebacks in South Africa.
Correspondents say that while the contents of Ms Madonsela’s report are unclear, Mr Zuma will be under increased pressure to resign if she reveals any adverse findings about him.
Government ministers Des van Rooyen and Mosebenzi Zwane, who have also denied being under the political influence of the Guptas, have joined the court action in support of Mr Zuma.
They are being challenged by a former MP of the governing African National Congress (ANC), Vytjie Mentor, who was a key witness in Ms Madonsela’s investigation.
She alleged in March that a member of the Gupta family had offered her the powerful public enterprise minister’s post in 2010 in exchange for business favours.
Ms Mentor also alleged that Mr Zuma was in another part of the Gupta’s family home in the upmarket Saxonworld suburb in Johannesburg when the offer was made.