1640s, "fatigue," noun of action from exhaust (v.) in sense of "drawing off" of strength. The etymological sense "act of drawing out or draining off" is by 1660s in English.
Entries linking to exhaustion
exhaust v.
1530s, "to draw off or out, to use up completely," from Latin exhaustus, past participle of exhaurire "draw off, take away, use up, empty," from ex "off" (see ex-) + haurire "to draw up" (as water), from PIE *heusio- "to scoop." Meaning "make weak or helpless, as by fatigue" is from 1630s. Related: Exhausted; exhausting; exhaustible.