The 27-year-old was one of four Brits still in contention on day five of the competition, but his campaign was ended with a valiant 7-6(4) 7-5 6-4 defeat.
Bedene immediately hit back after losing his break of serve in the sixth game, though Muller still had a big chance to take the opener when earning two set points.
After failing to take both a tie-break was required, which the Luxembourg pro took 7-4 thanks to three points on the spin.
The second set proved to be just as tight as both players snatched a break of serve early on, but Muller again managed to do just about enough to take it and move to within touching distance of victory with his second set point.
Muller then earned the only break in what proved to be the final set, edging out his opponent in the fifth to get himself over the line and set up a likely meeting with Rafael Nadal in round four.