Amakhosi overcame Golden Arrows and Stellenbosch in the previous rounds, and will play hosts to Baroka.
Ubuntu Cape Town will be looking to continue their giant-killing run after eliminating Polokwane City and AmaZulu when they take on Free State Stars.
Bloemfontein Celtic, who saw off Richards Bay, will travel to Maritzburg United.
It has also been confirmed that the final will take place on 19 May 2018 at the Cape Town Stadium.
Quarter-final draw in full:
Maritzburg United v Bloemfontein Celtic
Ubuntu Cape Town v Free State Stars
Cape Town City v Mamelodi Sundowns
Kaizer Chiefs v Baroka