Born in Reinach, Aargau, Müller began his international career in May 1962 with his first appearance at the Nürburgring 1000 km, driving a Porsche 718 RSK for Scuderia Filipinetti. He did not finish. The following year he raced a Ferrari 250 GTO for the same Swiss team and also competed in single-seater events, finishing fifth in the 1963 Pau Grand Prix in a Lotus-Climax — his only Formula One appearance in a non-championship race. He made his 24 Hours of Le Mans debut in 1964, sharing a Porsche 904 GTS with Claude Sage for Scuderia Filipinetti and finishing eleventh overall and fourth in the GT 2.0 class.
In 1966 Müller scored his first major victory, winning the Targa Florio in the number 148 Porsche 906 Carrera 6 alongside Willy Mairesse. Seven years later, in 1973, he repeated that achievement as part of the Martini Racing team, winning the Targa Florio again with Gijs van Lennep in a Porsche 911 Carrera RSR.
His Le Mans record over fourteen appearances featured two outright runner-up finishes. In 1971, driving the number 19 Porsche 917K for John Wyer Automotive Engineering alongside Richard Attwood, Müller finished second overall, two laps behind the winning Martini Racing 917K of Gijs van Lennep and Helmut Marko. In 1974, now himself part of Martini Racing, he again finished second at Le Mans, sharing the number 22 Porsche 911 Carrera RSR Turbo with van Lennep. His final Le Mans podium came in 1979, when he and Angelo Pallavicini and Marco Vanoli won the Gr. 4 GT class and finished fourth overall in a Lubrifilm Porsche 934.
During this period Müller competed under the banner of his own team, Herbert Müller Racing, as well as for Scuderia Filipinetti, JW Automotive Engineering, and Martini Racing. He also raced in the Canadian-American Challenge Cup and the International Championship for Makes, driving a variety of machinery including Ferrari 512s and a De Tomaso Pantera.
Between 1974 and 1976 Müller won three consecutive Interserie titles. The first two came with Martini Racing's Porsche — a 917/30 TC in 1974, when he scored five podiums in five races including three wins, and a 908/3 Turbo or 917/30 TC in 1975, when he again took five podiums in five races. His third title in 1976 was captured not with Porsche but in a Sauber C5-BMW for PP Sauber Racing, clinched without any race wins through consistent podium scoring. At the time of his death he remained a three-time Interserie champion.
Müller entered the 1971 Italian Grand Prix at Monza as a non-works Lotus entry under the banner of the Villiger Cigar Team Herbert Müller, with the car being a Lotus 72A powered by a Ford Cosworth DFV. He was listed as a DNA (did not attempt to qualify) and did not start.
Before the start of the 1981 1000 km Nürburgring, Müller announced publicly that the race would be his final competitive appearance. He was co-driving a Porsche 908 Turbo alongside his longtime friend Siegfried Brunn. On lap 17, at the Kesselchen section of the Nordschleife, a driver spun directly in front of him. Müller swerved to avoid the incident but collided heavily with an earth bank and was then thrown into a previously retired car driven by Bobby Rahal, causing a large explosion and fire. He was not wearing his safety belts and was killed in the initial impact. He was removed from the burning wreckage already dead. The race was stopped after 17 laps and was not restarted.
An earlier incident from his career illustrated his composure in extreme circumstances: while driving a Ferrari 512 in an Interserie race at the Nürburgring, Müller survived a fiery collision at the start that deposited his burning car in the pit lane next to a fire engine. He climbed out unaided and ran toward a firefighter to have the flames on his overalls extinguished.
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