1660s, "that which causes weariness," from French fatigue "weariness," from fatiguer "to tire" (15c.), from Latin fatigare "to weary, to tire out," originally "to cause to break down," from pre-Latin adjective *fati-agos "driving to the point of breakdown," with first half from Old Latin *fatis, which is of unknown origin but apparently related to affatim (adv.) "sufficiently" and to fatisci "crack, split." The second half is the root of agere "to set in motion, drive; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move").
Especially "the labors of military persons" (1776). Meaning "a feeling of weariness from exertion" is from 1719. Of metals or other materials under strain, from 1877.