In the present study, the quality characteristics of Feta cheese were investigated as a function of the packaging container (a stainless-steel tank (SST), a wooden barrel (WB), and a tin can (TC)) and ripening time. The results showed that the Feta cheese’s pH, moisture, and lactose decreased, while fat, protein, and salt increased (p < 0.05) during ripening with SST and WB, showing similar behaviors versus that of the TC container. For the proteolysis indices, % TN,% WSN, 12% TCA, and 5% PTA showed the highest values (p < 0.05) for cheeses packaged in WB, followed by those in SST and TC, with all increasing (p < 0.05) during ripening. The most abundant odor-active volatiles were free fatty acids, alcohols, and esters following the order SST > WB > TC on day 60. On day 60, the cheeses packaged in SST and WB showed higher (p < 0.05) hardness and fracturability values, as well as aroma scores, compared to those in TC, with both parameter values increasing with the ripening time.