"cause to hunger," c. 1400, famyschen, "alteration of famen (late 14c.), a shortening of Old French afamer (12c., Modern French affamer), from Vulgar Latin *affamare "to bring to hunger," from ad famem, from Latin fames "hunger" (see famine).
Ending changed mid-14c. to -ish under influence of ravish, anguish, etc. It also once had an intransitive sense and was so used by Shakespeare and Milton. Related: Famished; famishing.