early 13c., menour "Franciscan" (see minor (n.)), from Latin minor "less, lesser, smaller, junior," figuratively "inferior, less important," formed as a masculine/feminine form of minus on the mistaken assumption that minus was a neuter comparative, from PIE root *mei- (2) "small."
Some English usages are via Old French menor "less, smaller, lower; underage, younger," from Latin minor. Meaning "underage" is from 1570s. Meaning "lesser" in English is from early 15c.; that of "less important" is from 1620s. The musical sense is from 1690s. In the baseball sense, minor league is from 1884; the figurative extension is first recorded 1926.