mid-14c., from Old French incomprehensible or directly from Latin incomprehensibilis "that cannot be seized or appreciated," from in- "not" (see in- (1)) + comprehensibilis (see comprehensible). Related: Incomprehensibly.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1520s, "able to be contained," from Latin comprehensibilis, from comprehensus, past participle of comphrehendere (see comprehend). Meaning "able to be understood, capable of being conceived by the mind" is from c. 1600. Related: Comprehensibly; comprehensibility.