Amakhosi have drawn Acornbush United who ousted Cape Town City in the Last 32, while Bucs have been pitted against Free State Stars.
The Brazilians will host Golden Arrows in the Last 16.
Defending champions SuperSport will meet KwaDukuza United who knocked out Ajax Cape Town in the previous round.
Nedbank Cup last 16:
Chippa United vs Polokwane City
KwaDukuza United vs SuperSport United
Bloemfontein Celtic vs Mbombela United
Free State Stars vs Orlando Pirates
Jomo Cosmos vs BidVest Wits
Baroka FC vs Platinum Stars
Mamelodi Sundowns vs Lamontville Golden Arrows
Acornbush United vs Kaizer Chiefs
Download our app and read this and other great stories on the move. Available for Android and iOS.