The Pro14 Rainbow Cup will be split into two separate tournaments after no solution was found that would allow the South African teams to enter Britain and Ireland due to the coronavirus pandemic.
The Sharks, Stormers, Lions and Bulls had been due to join the 12 Pro14 teams in a six-round competition, starting on Friday and culminating in a final on June 19.
But the South African sides will now play each other on home soil in what could be yet useful warm-up games ahead of the British and Irish Lions tour in July and August that features three Tests against the world champion Springboks.
South Africa have not played an international match since beating England to win the 2019 World Cup final in Japan.
The intention had been for the South African franchises to travel to Europe for rounds four to six, but logistical obstacles caused by Covid-19 mean they will now play in Rainbow Cup SA instead.
The existing PRO14 teams will proceed with their scheduled fixtures.
"All options for the South African teams to travel to Europe safely were explored and exhausted by the league," said a Pro14 statement. "This is due to the heightened restrictions caused by South Africa's presence on the red list of the territories involved."
It had been thought that the competition could pave the way for the South African franchises to join an expanded Pro14 on a more permanent basis.
"This decision will have no impact on the long-term partnership between Pro14 Rugby and SA Rugby and more details about those plans and league structure for the ground-breaking 2021/22 season onwards will be made public shortly," said the statement.
Jurie Roux, the SA Rugby chief executive, added: "This is a huge disappointment, but time had simply run out. No stone was left unturned to try and find a solution to the challenges."