Mkhize also revealed that 174 new deaths had been recorded in the past 24 hours, taking the national total to 4,346.
The Western Cape has the highest number of deaths (2,429), followed by the Eastern Cape and Gauteng (both 726) and KZN (313).
Mkhize also reported 146,279 recoveries to date.
SA's figures come from a total of 2,232,738 tests, of which 38,114 were done in the past 24-hour cycle.
According to statistics-tracking website Worldometer, by the time Mkhize released the figures, SA is set to become just the ninth country to record more than 300,000 cases of Covid-19. The UK has recorded 290,133.
Within the next few days, given the massive spike in cases in recent days, SA is likely to pass Spain (303,033) and then Mexico (304,435).
As an indication of SA's relatively low mortality rate, it ranks 23rd in the world in terms of total deaths.
The UK has recorded 44,830 deaths to date, at a rate of 660 deaths per 1 million people. Comparatively, SA's 4,346 deaths is at a rate of about 70 per million.