The two men, aged 37 and 38, were tested and shown to have died as a result of the virus, said minister Joe Phaahla.
Mr Phaahla said that six cases had now been recorded in the country this year - two in Gauteng, and four in KwaZulu-Natal.
They were all classed as severe and required hospitalisation.
All diagnosed men were aged between 30 and 39, who had not been to other countries experiencing an outbreak - suggesting that the disease was being transmitted locally.
Mpox, formerly called monkeypox, is a viral infection transmitted through close contact.
Initial symptoms include fever, headaches, swellings, back pain, aching muscles, which can develop into a rash.
The World Health Organization (WHO) declared a public health emergency over an outbreak of mpox in 2022. Although this was ended last year, low levels of cases are still being reported in some countries.
"One death is too many, especially from a preventable and manageable disease," Mr Phaahla said on Wednesday, urging those with suspected symptoms to seek medical attention and help trace contacts.
Mr Phaahla said the six diagnosed patients had pre-existing immuno-deficiencies, and had contracted the disease since the start of May.
He noted that the virus has been reported in over 100 countries since 2022.
Two of those infected have been allowed to go home, while two remain in hospital.
Anyone who came into contact with a fatality will be monitored for 21 days.
The first human case was reported in Democratic Republic of Congo in 1970, and the disease remains endemic there, according to the WHO.
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