The deterioration of the Carica papaya L. fruit caused by Colletotrichum gloeosporioides highlights the importance of postharvest packaging for extending papaya shelf life. To this end, in this present study, pectin/gelatin-based food packaging (FPC) was enriched with Azadirachta indica hydroethanolic extract (HNE), obtained by pressurized liquid extraction (PLE) and microwave-assisted extraction (MAE). The HNE showed a high concentration of phenolic compounds, with values of 2893 mg GAE/100 g extract (PLE) and 3136 mg GAE/100 g extract (MAE). The packaging thickness incorporated with HNE (FPC + HNE) did not significantly differ (FPC + HNE-PLE: 0.10 ± 0.01, and FPC + HNE-MAE: 0.16 ± 0.04) from the packaging control (FPC: 0.11 ± 0.00). Nevertheless, the FPC + HNE exhibited enhanced elongation (FPC + HNE-PLE: 10.33 ± 0.2%, and FPC + HNE-MAE: 9.50 ± 0.2%) compared to FPC (8.00 ± 0.0%). Variations in water vapor permeability (FPC: 5.2 g·mm/d·m²·kPa, FPC + HNE-PLE: 2.0 g·mm/d·m²·kPa, and FPC + HNE-MAE: 6.9 g·mm/d·m²·kPa) and tensile strength (FPC: 13.76 ± 0.79 MPa, FPC + HNE-PLE: 16.45 ± 2.25 MPa, and FPC + HNE-MAE: 9.24 ± 2.01 MPa) values were observed among all samples. FPC + HNE-PLE resulted in 0% deterioration by Colletotrichum gloeosporioides over 15 days. The antifungal FPC + HNE-PLE provides a promising way to reduce postharvest losses and extend the shelf life of papaya fruit.