1580s, "subject to the authority of another," from Latin obnoxiosus "hurtful, injurious," from obnoxius "subject, exposed to harm," from ob "to, toward" (see ob-) + noxa "injury, hurt, damage entailing liability" (from PIE root *nek- (1) "death"). Meaning "subject to something harmful" is 1590s; meaning "offensive, hateful" is first recorded 1670s, influenced by noxious.
Obnoxious has two very different senses, one of which (exposed or open or liable to attack or injury) requires notice because its currency is now so restricted that it is puzzling to the uninstructed. It is the word's rightful or de jure meaning, and we may hope that scholarly writers will keep it alive. [Fowler]
Related: Obnoxiously; obnoxiousness.