Improving the storage of minimally processed mangoes represents a substantial challenge for packaging. For this purpose, thermoplastic starch (TPS) and its composites with bacterial cellulose nanoribbons (TPS/BC) are used as wrapping materials to prolong the shelf life of minimally processed mangoes. Commercial polyvinyl chloride stretch (PVC) films and unwrapped mangoes are used as the controls. The samples were stored at 75% RH and 5 °C for five and ten days. The films are removed after storage and subjected to mechanical tests and physical evaluation. The weight loss, firmness, total soluble solids, and total titratable acidity in the mangoes are tested to monitor fruit ripening. ATR-FTIR is used as an alternative nondestructive technique to examine fruit quality through changes in the sugar and organic acid contents. The results showed that TPS films reduced mango weight loss until the fifth day (2.84%), whereas the reduction in weight loss seen in mangoes wrapped with TPS/BC is even lower (13.18%). Therefore, even though both TPS and TPS/BC films can be used to prolong the fruit shelf life for five days, the latter is more effective. The elongations at break of both film samples remained constant over time, which means that these films can be used under stress conditions.