The draw was conducted in Johannesburg on Thursday night.
Orlando Pirates will welcome Bloemfontein Celtic, while Golden Arrows host Platinum Stars.
Jomo Cosmos, the only non-Premiership side left in the competition, will travel to Chippa United in their quarterfinal match.
Nedbank Cup draw:
Golden Arrows vs Platinum Stars
Kaizer Chiefs vs SuperSport United
Orlando Pirates vs Bloemfontein Celtic
Chippa United vs Jomo Cosmos
The dates and venues for the quarterfinals will be announced at a later stage.
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