A novel bio-based and compostable cellulose film (NF) was studied for the packaging of fresh baby spinach, with results compared to a petroleum-derived non-biodegradable polypropylene (PP) film, currently used to market the same product. Baby spinach is a leafy vegetable with high metabolic activity. A preliminary analysis of the product respiration rate was conducted to select the cellulose film grade. The chosen NF film ensures the optimal O2 and CO2 concentration in the headspace, performing even better than the conventional PP film. In fact, when the leafy vegetable is packed within PP, after 15 days of storage, no equilibrium value of gas concentration was reached, which, upon longer storage, might cause anaerobic conditions and off-odor development. Baby spinach leaves packed with NF film showed a slower decrement in texture properties and total antioxidant capacity during storage with respect to control samples, but also a larger weight loss, mostly due to the high-water permeability of the cellulose. However, water condensation upon storage was noted for both packaging materials. Analysis of mechanical, thermal, and barrier properties of the NF film before, during, and after use probed no deterioration of material properties, confirming the potentiality of this polymer for sustainable packaging of fresh leafy vegetables.