Three of the suspects said they have asylum status in South Africa.
Govindsamy Mariemuthoo, a police spokesman, refused to disclose a possible motive until the suspects made their next court appearance.
Court officials said that the next court appearance is July 14, in order to give investigators time to determine the suspects' immigration status.
Police last week dropped attempted murder charges against two others who were also arrested after the shooting.
Nyamwasa and his wife were returning to the upscale gated community where they live in northern Johannesburg when a lone armed man firedat him on June 19.
Nyamwasa's wife Rosette has accused Paul Kagame, the Rwandan president, of being behind the shooting.
Nyamwasa and Kagame were once allied but have fallen out, reportedly because Kagame sees his former military chief as a political rival.
Reporters Without Borders, a global media rights group, also alleged that the Tutsi-led government was cracking down on any opposition ahead of the presidential elections scheduled for August.
The recent murder of Jean-Leonard Rugambage,the deputy editor of the independent newspaper Umuvugizi, triggered allegations of a crackdown on the country's media and political opposition.
Human rights groups have criticised the government for planning the August polls while no significant opposition to Kagame's ruling Rwandan Patriotic Front (RPF) is in place.
Rwandan officials have accused Nyamwasa of trying to destabilise their government.
The Rwandan government says it has linked Nyamwasa to three grenade attacks in the country's capital on February 19 that killed one person and wounded 30 others.
South African police said earlier this year they had not arrested Nyamwasa because they do not have an extradition treaty with Rwanda.
Louise Mushikiwabo, Rwanda's minister of foreign affairs, said Rwanda does not kill its own people.
"There is this whole psyche that there is a crackdown in Rwanda, that tensions are reigning," Mushikiwabo said.
"People are taking advantage of the forthcoming elections to project this kind of situation, but I can assure you that the situation is created."