late 14c., short for baban (early 13c.), which probably is imitative of baby talk (cf. babble), however in many languages the cognate word means "old woman" (cf. Russian babushka "grandmother," from baba "peasant woman").
Crist crid in cradil, "moder, baba!" [John Audelay, c.1426]Now mostly superseded by its diminutive form baby. Used figuratively for "a childish person" from 1520s. Meaning "attractive young woman" is 1915, college slang. Babe in the woods is from 1795.