World governing body Fifa ordered the replay after the referee for the original game, Joseph Lamptey, was banned for manipulating the match.
The South African Football Association (Safa) had been considering an appeal but now says it agrees with Fifa.
However, it said it would appeal should the referee’s ban be overturned.
South Africa beat Senegal 2-1 in the original tie last year.
On Tuesday Safa said it “has decided on ethical and moral grounds that if this match was manipulated, we should replay it”.
It later added: “We have, however, noted that the official at the centre of all this controversy has appealed his case to the courts of law.
“If the courts overturn the decision, everything becomes null and void and Safa will reserve its right to challenge the decision of Fifa to replay the match.
“Safa’s zero tolerance on corrupt activities within football are well documented and it is in this light that we decided to comply with the Fifa directive.”
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Safa had been considering an appeal as it had not been consulted by investigators.
It means that South Africa are now bottom of Group D with a single point from three matches and now trail the third-placed Senegalese by four points.
Burkina Faso top the group with six points, just ahead of island nation Cape Verde on goal difference, with only the group winners qualifying for the World Cup in Russia.
Fifa will decide on 14 September on the exact date for the replay, which will take place in the international window in November – one month before the 2018 World Cup draw.
Neither South Africa nor Senegal have been accused of any wrongdoing.