1660s, of persons, "poorly dressed;" 1680s of clothes, furniture, etc., "of mean appearance, no longer new or fresh;" with -y (2) + shab "a low fellow" (1630s), extended from the original sense, "scabies." This is from Middle English shabbe "skin disease characterized by eruptions, itching, etc.," from Old English sceabb, the native form of Modern English scab (n.), which was influenced by Scandinavian (see sh-).
Shab (n.) survives in reference to a disease of sheep, but in Middle English shabbed meant "suffering from scabies, mange, etc." (from Old English sceabbed).
Shabby in the sense of "inferior in quality" is from 1805. The figurative meaning "contemptibly mean" is from 1670s. Similar formation in Middle Dutch schabbich, German schäbig "shabby." Related: Shabbily; shabbiness. Carlyle has shabbish "somewhat shabby."
Shabby-genteel "run-down but trying to keep up appearances, retaining in present shabbiness traces of former gentility," is attested by 1754. Shabaroon, shabberoon "disreputable person" is attested from c. 1700.