Before Ramaphosa's statement, the minister apologised for the public rage over the allegations, the latest in a series linked to coronavirus-related tenders that have angered a public suffering pandemic-induced economic hardship. Mkhize has denied any personal wrongdoing.
Ramaphosa, who has promised that graft during the Covid-19 pandemic will be dealt with harshly, said the special leave would enable Mkhize to answer an investigation into contracts between his department and service provider Digital Vibes.
Mkhize said: "I fully acknowledge and take personal responsibility for the public outrage that has been caused by this Digital Vibes contract."
"The negative discourse has ... tainted the team work of our government that is led by the president in our continued efforts to fight Covid-19. ... For all of this I want to unreservedly apologise," he added.
Minister of tourism, Mmamoloko Kubayi-Ngubane, will serve as acting minister of health until further notice, Ramaphosa's office said.
The Special Investigating Unit has said a probe it is conducting is nearing completion. The report will be given to Ramaphosa to decide on further action.
In May, Mkhize said a forensic investigation had found that the process of appointing Digital Vibes, headed by his former personal assistant and secretary, was irregular, as was more than R150m paid to the firm.
Daily Maverick, which first broke news of the contract in February, said the firm was appointed in late 2019 to provide communications services for the government's National Health Insurance rollout.
The scope of work was extended in March 2020 to include Covid-19-related communication.
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