Bafana, who were under Shakes Mashaba at the time, defeated Senegal 2-1 on match day two in the 2018 World Cup qualifiers.
Had South Africa won, qualification to the next round would have been in their own hands as Burkina Faso and Senegal drew 2-2.
Referee Joseph Lamptey was banned for life for match manipulation in South Africa's 2-1 win over Senegal past year, a match which included an absolutely bad penalty call.
Senegal and South Africa face a rematch in World Cup qualifying after the ref in their original game was found guilty of corruption.
The life ban for Lamptey was recently upheld by the Swiss-based Court of Arbitration for Sport (CAS).
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The Ghanaian official awarded a dubious penalty to Bafana just before halftime when Senegal's Kalidou Koulibaly was adjudged to have handled the ball in the box.
The FIFA Disciplinary and Appeal Committees imposed a lifetime ban on Lamptey for match manipulation, which has recently been upheld by CAS.
Senegal goes to Cape Verde on October 7, while South Africa hosts Burkina Faso.
A date has not been set for the make-up game, but Federation Internationale de Football Association says it will be played sometime in November. Only the top team qualify for next year's finals in Russian Federation.
"As stated in the FIFA World Cup regulations, this decision shall come into effect immediately but shall be subject to confirmation by the Organising Committee for FIFA Competitions at its next meeting, scheduled for 14 September", added the FIFA statement.