No.1 seed Hurkacz beat Daniil Medvedev and Roger Federer on the way to the semi-finals at Wimbledon, and previously beat Murray in Cincinnati.
Hurkacz is ranked No.13 in the world and is pushing for a place at the ATP Tour Finals, and he edged closer to a fourth career title by defeating Murray again in Metz.
The 24-year-old prevailed 7-6 (7-4) 6-3 over the former world No.1, who was playing in his first ATP Tour quarter-final of the year.
"Andy is an unbelievable competitor, he has achieved so much throughout his career," Hurkacz said. "He is coming back from a tough injury and playing at a very high level, so he is amazing and you can be inspired by his results."
Next up for Hurkacz is Peter Gojowczyk, who overcame Marcos Giron 3-6 6-1 6-3 and is backing up his recent US Open run in strong fashion.
The other last-four match will take place between French home favourite and No.3 seed Gael Monfils, who has reached his first tour semi-final since February last year, and Pablo Carreno Busta.
Carreno Busta, the No.2 seed from Spain, needed three sets to beat Holger Rune, while Monfils had an easier time of it against Nikoloz Basilashvili, winning 6-3 6-3.
At the Astana Open, No.2 seed Alexander Bublik beat Carlos Taberner 6-3 6-4, as he hunts a first singles title.
A crowd favourite in Kazakhstan, whom he has represented since 2016, Russian-born Bublik faces a semi-final against Soonwoo Kwon, who got past Laslo Djere.
No.5 seed John Millman succumbed to fellow Australian James Duckworth, who will face Ilya Ivashka for a place in the final.