Herbert, 28, won 7-6 (8/6), 6-4 to inflict a first-round exit on Monfils, who is ranked 27 places above him in the ATP rankings.
There was disappointment for the home crowd as German veteran Philipp Kohlschreiber suffered a second first-round defeat on home soil in the space of a week against American Steve Johnson.
Kohlschreiber, who also lost in the first round in Stuttgart last week, lost 6-3, 6-3 and missed the opportunity to set up a potential second round clash with compatriot Alexander Zverev.
Elsewhere, Moldova's Radu Albot came from behind to win 5-7, 6-1, 6-4 over Australia's Matthew Ebden.
Results from the ATP tournament in Halle on Monday (x denotes seeding):
Steve Johnson (USA) bt Philipp Kohlschreiber (GER) 6-3, 6-3
Radu Albot (MDA) bt Matthew Ebden (AUS) 5-7, 6-1, 6-4
Pierre-Hugues Herbert (FRA) bt Gael Monfils (FRA x5) 7-6 (8/6), 6-4