Mamelodi Sundowns will also travel to Polokwane to face Baroka.
Defending champions Bidvest Wits will also continue their title defence away to Maritzburg United.
The draw took place at the King Zwelithini Stadium after AmaZulu defeated Cape Town City 2-0 to take the last quarter-final spot.
Meanwhile, the Premier Soccer League confirmed that the Telkom Knockout final will be played at the Nelson Mandela Bay Stadium in Port Elizabeth on December 8.
TKO quarterfinal draw:
Maritzburg United vs Bidvest Wits
Kaizer Chiefs vs SuperSport United
Baroka vs Mamelodi Sundowns
AmaZulu vs Orlando Pirates