Citing a statement, Xinhua reported that Executive Mayor Cllr Herman Mashaba extended condolences to the families of the "two residents who tragically lost their lives during a stampede..."
The incident happened at a gate of the stadium that hosted the 2010 World Cup final, during a match between Soweto giants Kaizer Chiefs and Orlando Pirates.
The cause of the stampede is under investigation by the South African police.
"All gates have been opened to ensure crowd control and the game is proceeding without any further incident," the statement added.
Michael Sun, Member of Mayoral Committee (MMC) for public safety for Johannesburg, told Xinhua that the situation is calm and the injured were sent to local hospitals.