North Group winners Lancashire will host Glamorgan in the opening T20 Blast quarter-final on Friday, 1 August, at Old Trafford (18:30 BST).
The Red Rose County won 10 of their 14 group matches, while the Welsh side qualified fourth in the South Group.
On Saturday, 2 August, Surrey host Worcestershire (14:30 BST) before Essex take on Birmingham Bears (18:00 BST).
The final last eight tie, on Sunday, 3 August, will see Nottinghamshire play Hampshire at Trent Bridge (14:30 BST).
The four winners will go through to finals day at Edgbaston on Saturday, 23 August.
Lancashire, who have seen former England all-rounder Andrew Flintoff come out of retirement to play in the competition, have lost just two games in the competition this summer, less than any other county.