COVID-19 is already a highly contagious disease, spreading 10 times faster than most strains of influenza, but this new variant may spread even faster.
He said the country "cannot go through what we went through in the early days of the Aids pandemic".
There is no evidence to suggest the South African variant is more transmissible, causes more severe disease or increased mortality than Britain's variant or any other variant that has been sequenced in the world, said Mkhize.
By Thursday, South Africa had reported 954,258 infections and 25,657 deaths.
The British minister's words "have created a perception that the variant in South Africa has been a major factor in the second wave in UK", Mkhize said.
A similar result was found in the new strain found in South Africa, which was initially believed to be more transmissible among young people.
Under the rules, which come into effect from Friday, foreigners who have been in the United Kingdom in the last two weeks will also be barred from boarding Brazil-bound flights.
It can not be said with certainty whether the mutation is more infectious than previously detected strains, Africa CDC head John Nkengasong said, as studies were still being carried out.
"It's not going to have a negative impact politically on relations between South Africa and United Kingdom, but I think what is important is that moving ahead it's quite clear from the South Africa perspective, that it becomes very hard to return to some kind of normality when it comes to economic planning, when it comes to worldwide travel because we see this stop and start approach to the global economy".
"There's certainly anecdotal reports of explosive outbreaks for that virus and very steep increases in case numbers".
While France eased its travel restrictions, Brazil has become the latest country to implement a ban on flights from the UK.
For the first time since confirming sub-Saharan Africa's first virus case in February, Nigeria is in the spotlight as infections surge. "This has led to an unusual delay with testing, but we're working around the clock", with many colleagues cutting short their holidays and returning to work.
Nigeria, Africa's most populous country with more than 200 million people, has seen fewer coronavirus cases than many others on the continent.
On Christmas Day, the country recorded 14 796 new cases, bringing the cumulative number to 983 359.
- S Pen Support for Galaxy S21 Ultra Confirmed by FCC
- Sussexes' Christmas card features tree decorated by Archie
- Britain and European Union release full text of post-Brexit trade deal
- Talent Not an Issue for England's New Manager
- PM Modi is the true well-wisher of farmers: Amit Shah
- PS5 Custom Faceplates Announced By Dbrand, Challenges Sony to Sue
- Christmas Eve Service Presented by United Churches of Thunder Bay
- Alibaba shares fall after reports of anti-monopoly probe by China
- Harden fined but avoids suspension for National Basketball Association protocol violation
- Minus (some) refunds, Cyberpunk 2077 has already sold 13 million copies