These three categories make up 1,163 (or 37%) of the 3,142 cases where the age and gender of the infected person was known.
The figures were correct as at Sunday,, the department said.
The statistics also revealed that 83 children aged 10 or younger had been infected, while two people aged 91 or older had tested positive for the virus.
Health minister Dr Zweli Mkhize had previously announced that the country's oldest Covid-19 death was that of a 91-year-old, and the youngest was a 46-year-old.
When it came to men, the age group impact followed a similar pattern as women.
Worst hit were those in the 31 to 40 age group, with 309 cases, followed by the 21 to 30 category (259 cases). The third worst hit was the 51 to 60 age-group category, with 254 cases.
The full breakdown was provided as follows: