The continent currently has the lowest uptake of Covid shots in the world.
The company behind the new vaccine - Afrigen Biologics - says it hopes to start clinical trials in November.
Moderna previously said it would not enforce the patents on its vaccine, allowing scientists in Cape Town to make their own version of it.
The researchers were backed by the World Health Organization (WHO).
Petro Terblanche, director of Afrigen Biologics, said they were starting small, but had ambitions to scale up quickly.
"We have used the sequence, which is the same sequence as the Moderna vaccine 1273," she told the BBC.
"This is part of a global initiative to build capacity and capability in low and middle-income countries to become self-sufficient."
The shot being copied is a messenger RNA vaccine made by US firm Moderna. Pfizer-BioNTech also made its vaccine using the same technology. They were some of the first Covid vaccines to be authorised for use around the world.
This type of vaccine teaches cells how to make a protein that will trigger an immune response inside our bodies, rather than putting a weakened or inactivated germ into the body.
The company's chief scientist, Dr Caryn Fenner, called the achievement "really significant".
"It puts the power in our hands to be able to produce our own vaccines for the future, to be ready for further pandemics, to produce clinical trial material on African soil and then to look at other diseases of relevance in Africa."