Pool 5 winners Edinburgh secured a last-eight spot by beating Montpellier seven days ago, while Munster topped Pool 2, courtesy of a narrow victory over Exeter.
The game, which has a 12.45pm kick-off, will shown live on Channel 4 and BT Sport.
It is one of three quarter-finals that day.
It will be followed by top seeds and twice European champions Saracens tackling Glasgow at Allianz Park, kicking off at 3.15pm.
The Warriors were in the same pool as Sarries but will meet them again due to them being bottom seeds.
The Glasgow game will be live on BT Sport.
Later on Saturday Champions Cup holders Leinster host Ulster at the Aviva Stadium (kick-off 5.45pm).
An all-French clash between Racing 92 and Toulouse will take place on Sunday March 31 (kick-off 3.15pm).
Champions Cup quarter-finals
Saturday March 30
Edinburgh v Munster (1245)
Saracens v Glasgow (1515)
Leinster v Ulster (1745)
Sunday March 31
Racing 92 v Toulouse (1515)