Home Postcode finder VIC Narrung Narrung postcode VIC Narrung is a locality in Victoria covered by postcode 3597. Postcode 3597 State or territory Victoria (VIC) Region Vic Far Country Add a free Narrung business listing Be the first listing in Narrung Common questionsWhat is the postcode for Narrung?Narrung, VIC has the postcode 3597.What state is Narrung in?Narrung is in Victoria (VIC).Does postcode 3597 cover more than one suburb?Yes. Postcode 3597 covers 6 localities, so the postcode alone does not identify Narrung. Browse other postcodes in Victoria, or widen the search to every Australian postcode.