The incident took place during a match between Orlando Pirates and Kaizer Chiefs. Police confirmed the deaths and said several other people were injured.
In a statement cited by an online football website KickOff, the match sponsors Carling Black Label also confirmed "two fatalities caused by blunt force trauma".
Fans have also questioned the decision to continue with the match regardless of the fatal stampede. Tickets for this match were sold out two weeks in advance and match organisers believe everything was in place for a safe event on Saturday, July 28.
Operations Manager for Gauteng EMS Colin Errakiah says one person is in a critical condition in hospital.
In 2001, 43 people were crushed to death when a reported 30,000 additional fans tried to cram into Ellis Park Stadium, which has a capacity of 60,000.
The situation is calm at the moment, Sun said.
Players and officials inside the stadium were not alerted to the troubles outside with Chiefs running out 1-0 winners after 90 minutes.
South African Football Association (SAFA) said it was "deeply saddened by the tragedy". "What happened to at FNB Stadium is very unfortunate", Jordaan added.