The use of stretch films as a second skin over fruits is a common technological solution to prevent their deterioration during postharvest storage. However, these films pose an environmental problem, and the management of this waste is a challenge. To address this issue, a new biodegradable polymer composed of a blend of butylene adipate-co-terephthalate and polylactic acid (PBAT-PLA) called Nature Fresh® has been developed to produce stretch films suitable for post-harvest use without environmental concerns. Pomegranate is a fruit that is highly sensitive to Chilling Injury (CI) at temperatures below 5 °C. To evaluate the suitability of Nature Fresh® film for pomegranate packaging, two cultivars with different sensitivity to CI, 'Bigful' and 'Mollar de Elche', were wrapped with the film and stored for 56 days at 2 °C plus 2 days at 20 °C. Control groups included fruits without film and fruits wrapped with stretch film made of linear low-density polyethylene (LLDPE), which is commonly used in post-harvest storage. Pomegranates packed in PBAT-PLA and LLDPE films showed similar evolution in the appearance of internal and external husk CI, respiration rate, ion leakage, total polyphenol, and anthocyanin content, these parameters being lower than in control fruit. However, due to differences in water vapor and gas permeability between the two films, weight loss and firmness reduction were significantly higher in pomegranates wrapped in PBAT-PLA compared to LLDPE, but this did not impact any detrimental effect on overall appearance. Internal CI was significantly (P < 0.001) positively correlated with fruit respiration rate, ion leakage, weight loss, total polyphenol, and anthocyanin content; while it was negatively correlated with fruit firmness, skin and aril color, soluble solids, acidity, and maturity index. In summary, the use of PBAT-PLA film presents a feasible substitution to LLDPE on maintaining the quality of pomegranates during post-harvest storage, while also aligning with worldwide initiatives aimed at decreasing plastic waste.