Bafana Bafana won the match 2-1 after official Joseph Lamptey gave a penalty for a handball against defender Kalidou Koulibaly, when the ball had clearly struck him on the leg, with the score level at 0-0.
The November 2016 result is the only win collected by bottom side South Africa in Group D of African qualifying, with Senegal above them in third place, a point behind joint-leaders Burkina Faso and Cape Verde after September's fixtures.
FIFA's decision to replay the game comes after the lifetime ban handed to Ghanaian official Lamptey for "match manipulation" was upheld by the Court of Arbitration for Sport.
"The match will be replayed within the November 2017 international window, with the exact date to be confirmed in due course," a FIFA statement said.
"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 September 14."
The South African Football Association (SAFA) has denied all wrongdoing but will consider FIFA's report before deciding whether or not to launch an appeal.
"SAFA is studying the contents of the report and will issue a statement on intentions to challenge that decision," the organisation said.
"SAFA wishes to also state categorically that it was in no way involved with any wrongdoing related to the actions of the referee, as stated in the FIFA report."