1590s, "a 'vocal gesture' expressing the action of puffing anything away" [OED], used as an exclamation of dislike, scorn, or contempt, first attested in Hamlet Act I, Scene III, where Polonius addresses Ophelia with, "Affection! pooh! you speak like a green girl, / Unsifted in such perilous circumstance. / Do you believe his tenders, as you call them?" But the "vocal gesture" is perhaps ancient.