World No.10 Ruud prevailed 7-5 6-4 over the three-time grand slam winner, rolling to victory after a shaky start.
Murray broke Ruud in the 22-year-old's second service game of the match, but could not maintain the advantage as Ruud converted five of six break points in the match.
Ruud will face No.9 seed Lorenzo Sonego, who defeated Sebastian Korda 6-4 6-3, saving six of seven break points against his own serve while converting all three of his chances on Korda's.
No.4 seed Denis Shapovalov defeated Taylor Fritz 7-6 (9-7) 6-2, saving six set points in the process.
The Canadian moves on to a quarter-final meeting with Cameron Norrie, who downed Daniel Evans 7-6 (7-3) 6-3.
Grigor Dimitrov dominated August Holmgren 6-1 6-1 in 56 minutes, winning 83 per cent of his service points.
Dimitrov next faces Aslan Karatsev, who rallied to upset No.5 seed Hubert Hurkacz 5-7 6-4 6-2.