In a draw which was conducted on Friday night, the Sea Robbers were drawn in Group B while the Brazilians were drawn in Group A.
The Soweto giants were pitted alongside FC Platinum, Horoya SC, and Esperance in a group consisting of four teams.
Horoya in the same group as Sundowns last season, while Pirates would be more familiar with Esperance having faced them in the past.
FC Platinum would certainly not be a walk in the park, but this is one team that Pirates would fancy their chances more considering their record in the competition.
Sundowns, who won the Caf Champions League trophy in 2016, were drawn alongside Wydad Casablanca, whom they faced and lost to in the 2017 edition.
Pitso Mosimane's men will also come up against Lobi Stars of Nigeria as well as Asec Mimosas of Cote d'Ivoire.
South African football fans were excited at the prospect of seeing both Sundowns and Pirates in action against each other in the Caf Champions League.
However, both teams would have to wait for the group stages to see that happen provided the two teams advance to the next phase of the competition.
Caf Champions League group stage draw in full:
Lobi Stars (Nigeria), Wydad Casablanca (Morocco), Asec Mimosas (Cote d'Ivoire), Mamelodi Sundowns (South Africa).
Platinum FC (Zimbabwe), Horoya FC (Guinea), Orlando Pirates (South Africa), Esperance de Tunis (Tunisia).
TP Mazembe (DR Congo), Club Africain (Tunisia), Ismaily SC (Egypt), CS Constantine (Algeria).
Al Ahly (Egypt), Simba SC (Tanzania), JS Saoura (Algeria), AS Vita Club (DR Congo).