Pirates, who were defeated in the 2018 final, were amongst the seeded teams which finished in the top half in the Premier Soccer League (PSL) last season.
The Buccaneers have been pitted against tournament debutants Stellenbosch FC in the Round of 16.
Record 13-time Telkom Knockout champions Chiefs finished outside the top eight in the league last season and they were placed in the pot containing the unseeded sides.
Amakhosi have been drawn against the 2016 winners Cape Town City in a mouthwatering encounter.
Sundowns' Tshwane rivals SuperSport United are set to square off with the defending Telkom Knockout champions Baroka FC.
The PSL is expected to announce fixture dates, venues and kick-off times at a later stage.
The 2019 Telkom Knockout draw results
Maritzburg United vs Bidvest Wits
Cape Town City vs Kaizer Chiefs
Mamelodi Sundowns vs AmaZulu
SuperSport United vs Baroka
Orlando Pirates vs Stellenbosch