South African police said they have no information on the shooting.
Our correspondent said that Paul Kagame, the president of Rwanda, and Nyamwasa had fallen out.
"He [Nyamwasa] wasn't happy that those who opposed Kagame were detained and harassed and spoke up about that and other cases of corruption happening in Rwanda at the moment.
"He was then forced to flee the country and has been in hiding in South Africa for the past four months."
The Rwandan government has linked Nyamwasa to three grenade attacks in Kigali, Rwanda's capital, on February 19, which killed one person and injured at least 30 others.
The authorities have accused Nyamwasa of trying to destabilise Rwanda while he was in the country, and while he was in India, where he served as Rwanda's ambassador.
South African police said earlier this year they had not arrested Nyamwasa because they do not have an extradition treaty with Rwanda.