He said that while KZN numbers were the third highest in the country, this could change in the coming weeks.
"During next week, KZN will have more positive patients than what the Western Cape had. In some of the [recent] days in KZN, there are more positive cases per 24 hours than Gauteng. The province needs to be ready. KZN is on course for a surge."
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Mkhize said the Eastern Cape, Western Cape and Gauteng were on a decline, but that KZN's numbers would surge.
"KwaZulu-Natal will carry the upward trend and will have much bigger numbers."
Alcohol ban will remain
Mkhize said the alcohol ban would remain, but did not speak to the science behind the decision, simply saying that alcohol was closely linked to trauma cases which flooded much needed hospital beds.
Our focus is about the health of the nation. Where we think certain practices will compromise the health of our people, we will not hesitate and stand on the side of the health of our people.
Mkhize added: "We take a view based on what we see with the situation on the ground. When things changes and we think it will be safe to ease up certain things, we will certainly do that."
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He said an intensive care specialist pointed out that fewer trauma patients had helped.
"He said it makes it easier for them to work. Our position is very simple. When we see that the numbers are improving and there is no pressure for beds, then we will consider this. We have not come to that point yet."
Mkhize said it was also difficult to speak on the alcohol matter because government was taken to court over its ban.
"As far as we are concerned, there are real reasons why we support the suspension of alcohol. Bed numbers were actually getting filled and therefore we were running out of beds. All the hospitals showed us the figures. Everybody knows this. There are avoidable situations... we must focus as South Africans."