"Following extra information from FIFA, we resolved on moral and ethical grounds that we cannot benefit from corrupt activities," a national football association statement said.
"Therefore, we have decided to comply with the FIFA directive to replay the match against Senegal on a date to be decided."
Referee Joseph Lamptey awarded South Africa a non- existent penalty which they converted en route to a 2-1 home victory over Senegal in Group D last November.
The other South African goal was also controversial with the match official still ordering Senegalese players to retreat for a free-kick after it was taken.
FIFA gave Lamptey a life ban for match manipulation and his appeal to international sport judicial body CAS was rejected.
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