Karim also said the AstraZeneca vaccine would in future be rolled out in a "stepped manner" to assess its ability to prevent severe illness.
The country, which has recorded the most coronavirus infections in Africa and more than 46,000 deaths, had planned to start offering healthcare workers the AstraZeneca jabs soon but put that plan on hold on Sunday.
A government factsheet published on Monday said the J&J vaccine would be offered from mid-February. A senior health official said J&J had agreed to speed up deliveries so the first doses would become available around the end of the week.
Preliminary trial data showing the AstraZeneca shot does not significantly reduce the risk of mild-to-moderate illness caused by the more contagious 501Y.V2 variant first identified late last year was a disappointment not just to South Africa, but to the continent as a whole.
The 501Y.V2 variant is believed to have spread to nine other African countries, according to a World Health Organization (WHO) epidemiological report last week.
The AstraZeneca vaccine is seen as one of the best suited to weak African health systems as it can be stored at refrigerator temperatures, rather than the ultra-cold temperatures needed for shots from Pfizer/BioNTech.