early 13c., in frere menour "Franciscan friar," literally "minor friar," from Latin minor "less, lesser, smaller, junior," figuratively "inferior, less important," which was formed as a masculine/feminine form of minus on the mistaken assumption that minus was a neuter comparative, from PIE root *mei- (2) "small." Compare minor (n.). In some cases the English word is from Old French menor "less, smaller, lower; underage, younger," from Latin minor.
Meaning "underage" is from 1570s. Meaning "lesser or smaller (than the other)" in English is from early 15c.; that of "comparatively less important" is from 1620s. The musical sense is from 1690s in reference to intervals (and to tonalities and scales characterized by a minor third), so called because the interval is lesser or shorter than the corresponding major interval. Of triads or chords by 1797; their emotional effect is notable mournful, mysterious, gloomy, or wistful, hence figurative and extended senses. In the baseball sense, minor league, made up of teams below the major league, is from 1884; the figurative extension of that is recorded by 1926.