The resident lives in the Soho and Victoria ward of Smethwick.
It is a single case and further testing of contacts is now underway.
It comes only weeks after a case of the variant was discovered on the Oldbury and Tipton border.
Lisa McNally, director of public health at Sandwell Council, said: “There is no evidence at this stage that this case has any links to another case of the South African variant found in the Oldbury/Tipton area or any cases found in other neighbouring areas.
“Extensive contact tracing is already underway and we will know more in the next day or two.
"This will then indicate whether further testing in the area is needed.
“There will not be any extra restrictions put in place. Schools and workplaces in the area can continue to operate as normal.
“However, this serves as a reminder that this pandemic has not gone away. We all need to remain vigilant in keeping 2 metres distance from others, wearing face coverings and washing our hands.”
A spokesman for Sandwell Council said if further testing is required in the area, residents will be informed over the coming days.