Grant Shapps told the BBC the UK "acted immediately" with a "safety first" approach by placing six countries on its red list to restrict travel. Susan Hopkins, the UK Health Security Agency's chief medical adviser, said it was the "most worrying" variant yet. No cases have been confirmed in the UK.
From midday travellers from South Africa, Namibia, Zimbabwe, Botswana, Lesotho and Eswatini will have to self-isolate for 10 days, with those arriving after 04:00 GMT on Sunday required to quarantine in a hotel.
All flights from the six countries are also being suspended until the hotel quarantine system is in operation.
South Africa, Hong Kong and Botswana have identified just 59 cases of the variant, known as B.1.1.529, so far, while Israeli media also reports one case has been identified from a traveller.
Mr Shapps paid tribute to South Africa's fast and transparent response, and said of the UK's decision to restrict travel: "This is a safety-first approach."
He said the UK "acted immediately" because "we can't take risks when it comes to something that could defeat the vaccine", as scientists fear may be possible.
People who have returned from the six countries in Africa in the last 10 days will be contacted and asked to take a PCR test, but Mr Shapps said, with only a small number of cases identified worldwide, they do not expect to detect any in the UK.
"We know from lots of experience now that you can never stop these things but early action buys you more time," Mr Shapps said.
Health Secretary Sajid Javid is due to update the House of Commons about the Covid situation at 11:00 GMT.
Scientists say the variant has 50 mutations overall and more than 30 on the spike protein, which is the target of most vaccines and the key the virus uses to unlock the doorway into our body's cells.
Prof James Naismith, director of the Rosalind Franklin Institute at Oxford University, said: "It's bad news, but it's not doomsday."
The variant would "almost certainly" make vaccines less effective, but they would still work to some extent. New drugs to treat Covid-19 would not be affected by the variant, he suggested.