It is one of 11 cases of the variant in the UK that have no known links to travel or previous cases - prompting concerns that the variant is spreading among communities just as infection rates had started to fall.
There is no evidence that the South African variant is any more harmful than other coronavirus strains but it is thought to spread between people more easily.
The person who tested positive for the variant in Walsall is self-isolating at home and has not been out of the country, leader of Walsall Council Mike Bird said.
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He said the council was first made aware of a possibility of the new variant in Walsall on Thursday last week.
Other cases have been discovered in three different areas of London, Broxbourne in Hertfordshire, Maidstone in Kent, Woking in Surrey and Southport in Merseyside.
Efforts are now being made to curb the spread of the variant by setting up mass testing in the affected areas, meaning Walsall Council is now hoping to test more than 10,000 who don't have symptoms in the coming weeks.
People over the age of 18 who live or work in WS2 - which includes Birchills, Pleck, Bescot and Walsall Manor Hospital - will be strongly encouraged to take a Covid-19 test this week.
Home testing kits will be offered and a mobile testing unit could be in place at Forest Arts Centre, with all positive tests set to be analysed to identify any further spread of the new variant.
Councillor Bird added: "We've got a case of the South African variant in Walsall in WS2. We are aware of it and looking to get mass testing in WS2 area and we're encouraging everybody to take a test because we need to see how far it's spread.
"We were alerted by Public Health England that there is an individual who has not been out of the country so we have to identify how this has occurred so we have to look at ways to contain it.
"We don't want people to panic we will do what is necessary and as far as we're aware it's the only one."
It is not yet known whether the Oxford University/AstraZeneca vaccine will be effective against the variant, although other vaccines have shown promising results.
Experts advising the Government said they did not think the current vaccines would need to be tweaked to deal with any spread of the South African variant.
To date, 105 cases of the South African variant have been identified in the UK since December 22 but all of those had links to travel.
Experts believe the 11 new cases may also have second or third generation links to travel but detailed investigations have not identified any such links.
'Please get tested'
Stephen Gunther, director of public health in Walsall said: “The more cases of the variant we find, the better chance we have at suppressing it. Please help to keep your community safe by getting tested so we can find the variant and protect you and your loved ones.
“There is currently no evidence that this variant causes more severe illness, or that the regulated vaccines would not protect against it, but research indicates that it does transmit from person to person more easily.
“We know that mutations form a part of the virus cycle and the scientific community is well prepared to analyse new variants and assess what action may need to be taken.
“If a person tests positive, has any symptoms, or is contact traced following contact with someone who tests positive, they should self-isolate immediately.”
Councillor Stephen Craddock, portfolio holder for health and wellbeing in Walsall, added: “If you are asked to be tested, please do take up the offer. It’s quick, easy and painless and, put simply, you could save lives by doing so.
“There will be a minimum of one additional Mobile Testing Unit in the borough. However we recognise that not everyone has access to a car and may feel anxious about using public transport, so plan to expand that offer as well as offering home testing kits, which come with clear instructions.
“We would very much appreciate the assistance of faith and other community leaders and trusted local voices in reaching our communities and encouraging them to get tested.”
The infection rate for the West Midlands currently stands at 350.4 cases per 100,000 people. This is the second highest regional rate in England but it is down week-on-week from 528.5, and is the lowest it has been since December 28.
All local areas in the region are seeing a drop in rates, with the largest falls in Wolverhampton (down from 790.2 to 484.1) and Sandwell (875.3 to 574.8) which has the third highest rate in the whole of England.