This was the second American Humbert, 27, has knocked out in Basel following his first round defeat of Sebastian Korda 24 hours earlier.
The French number one left-hander's reward is a quarter-final match-up against US qualifier Reilly Opelka.
Last Sunday, the world number 24, Humbert, reached the final of the Stockholm ATP 250 tournament, where he was beaten in two sets by Norway's Casper Ruud.
Ruud, the fourth seed, downed veteran home hope Stan Wawrinka 6-4, 7-6(5) in Basel to set up a quarter-final date with Alejandro Davidovich Fokina.
Defeat for Fritz came on the back of his battling three-set first-round win over this month's Shanghai Masters champion Valentin Vacherot.
Basel second seed Ben Shelton was also sent packing, 6-3, 6-4 by Spain's Jaume Munar, who faces fifth-seed Felipe Auger-Aliassime in the last eight.