This was after Sundowns advanced to the last four after defeating City 2-1 in a quarter-final encounter which was played in the Mother City.
They joined fellow Premier Soccer League (PSL) sides Free State Stars, Maritzburg United and Chiefs in the semi-finals.
The 2015 Nedbank Cup champions Sundowns were pitted against Maritzburg United during the draw which was conducted at the Cape Town Stadium.
Maritzburg booked their place in the last four after winning 2-1 against Bloemfontein Celtic at the Harry Gwala Stadium in Pietermaritzburg on Saturday.
Record-13 Nedbank Cup champions Chiefs will lock horns with a stubborn Free State Stars side for a place in the final.
Amakhosi edged out Baroka FC 1-0 in a quarter-final match which was played at the Nelson Mandela Bay Stadium in Port Elizabeth on Saturday.
Stars progressed into the semi-finals after beating National First Division (NFD) side Ubuntu Cape Town 4-2 on penalties following a 1-1 stalemate at the Athlone Stadium in the Mother City in another game which was played on Saturday.
The matches are scheduled to take place the weekend of April 20.
Nedbank Cup semi-finals:
Maritzburg United v Mamelodi Sundowns
Kaizer Chiefs v Free State Stars