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)