The stampede occurred when a number of fans attempted to gain entry into the Carling Black Label Cup encounter between Kaizer Chiefs and Orlando Pirates at FNB Stadium in Johannesburg.
Players and officials inside the stadium were unaware of the incident and the match was allowed to continue with Kaizer Chiefs winning 1-0.
SAFA president Danny Jordaan said in a statement: "We offer our sincere condolences to the family members of those who lost their lives."
"We are going to ask for a full report and institute a full investigation on what transpired and the cause for the stampede."
"I would also like to wish the injured speedy recovery. A football match is supposed to be a place of entertainment. What happened to at FNB Stadium is very unfortunate."