The former Zimbabwean first lady is accused of assaulting model Gabrielle Engels in a Sandton hotel in 2017.
"I really do think it's the correct step by the NPA and that they should now pursue this because to apply for extradition is one thing, to ensure that the process runs to its finalisation is another. But it's a very positive step to ensure that justice is done and that nobody is above the law and that Grace Mugabe should come back to South Africa and face the law," says the head of AfriForum's private prosecutions unit, Gerrie Nel.
Nel adds that no-one should be above the law due to their political status.
"When this matter happened, we immediately thought that because of the political profile of the Grace-Engels matter that there might be political interference. We just wanted to ensure that somebody is not sheltered from prosecution because of political influence and the political status."
The former first lady allegedly attacked Gabrielle Engels using an electrical extension cord at an upmarket hotel where Mugabe's two sons were staying.
At the time, Grace Mugabe was granted diplomatic immunity by the South African government, allowing her to leave the country.
A court later scrapped the immunity, labelling the decision by the foreign ministry as "inconsistent with the Constitution".
Nel warns that AfriForum is ready to file papers to privately prosecute Mugabe, should the NPA fail to do so.