The Betway Premiership side managed to avoid a match-up with competition holders Pyramids and Al Ahly after the draw was conducted on Tuesday.
They ended in second place in Group C behind Al-Hilal and will now face the Group D winners.
While Downs recorded nine wins from their six group games, the Whites claimed 11 points, to claim top spot ahead of ES Tunis, Petro de Luanda and Simba SC.
Sundowns host the first leg the weekend of 13-15 March, ahead of the return leg in Bamako a week later.
Pyramids will, meanwhile, face Morocco's Royal Armed Forces, while Al Ahly play Esperance.
All the quarter final ties:
Renaissance Berkane (Morocco) v Al Hilal (Sudan)
Esperance (Tunisia) v Al Ahly (Egypt)
Mamelodi Sundowns (South Africa) v Stade Malien (Mali)
Royal Armed Forces (Morocco) v Pyramids (Egypt)
Orlando Pirates and Mamelodi Sundowns will headline this week's Betway Premiership action when they meet at the FNB Stadium in Johannesburg on Wednesday in a clash that could shape the title race.
Mamelodi Sundowns have been drawn against Malian surprise package Stade Malien in the quarterfinals of the CAF Champions League.
Mamelodi Sundowns head coach Miguel Cardoso has called on the Premier Soccer League to consider rearranging their upcoming Betway Premiership fixtures to accommodate their CAF Champions League campaign.
We take a look at five players that could have a big influence on the result of Wednesday's Betway Premiership clash between Orlando Pirates and Mamelodi Sundowns.
