Pomegranate is a sensitive fruit to chilling injury (CI) during storage at temperatures below 7 °C. However, sensitivity of pomegranate to CI is dependent on cultivar and exposure times to low temperatures. In this work, the sensitivity to CI of six pomegranate cultivars (Punica granatum L.) ‘Wonderful’, ‘Kingdom’, ‘Bigful’, ‘Acco’, ‘Purple Queen’, and ‘Mollar de Elche’, was evaluated after 30 d at 2 °C plus 2 d at 20 °C. Among cultivars, there was a great variability in the sensitivity to the appearance of CI symptoms. ‘Kingdom’ cultivar was the most CI sensitive and ‘Mollar de Elche’ cultivar was the least sensitive cultivar. CI symptoms were greater in the internal part of the skin than in the external part, although no correlation was found between ion leakage (IL) and CI severity after cold storage. However, both, external and internal CI index were correlated with the IL at harvest, with Pearson correlation of 0.63 and 0.80, respectively. In addition, this variability to CI among cultivars could also be due to composition and tissue structures in arils and peel. The solute content of the arils (anthocyanins, sugars, and organic acids, in particular citric acid), showed high correlations with CI sensitivity, with Pearson correlations (r) of 0.56 for total soluble solids, 0.87 for total acidity, 0.94 for anthocyanins, −0.94 for oxalic acid, 0.87 for citric acid, 0.62 for tartaric acid, −0.91 for malic acid, 0.8 for sucrose, and 0.71 for glucose, which can leak to the inner surface of the peel causing browning reactions. In addition, the high peel Ca/K ratio could play an important role on increasing fruit tolerance to CI, since it was negatively correlated with the internal and external CI indexes.