The November 2016 tie, which will be restaged in November, was won by South Africa 2-1 after Ghanaian referee Joseph Lamptey awarded them a controversial penalty.
Lamptey was initially suspended for three months by African football's ruling body CAF for awarding a penalty for a non-existant handball", with FIFA handing down the life ban in March.
News of the rematch comes as a boost for Senegal, who are placed third, one point behind Cape Verde and Burkina Faso in African zone qualifying Group D, with two games to go.
FIFA explained the decision to replay the game had come after sport's highest court CAS had confirmed "the lifetime ban of match referee, Joseph Lamptey, for match manipulation, the ruling imposed by the FIFA Disciplinary and Appeal Committees".
The statement added: "The match will be replayed within the November 2017 international window, with the exact date to be confirmed in due course.
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