Burn wound management remains challenging due to infection risk, delayed healing, and limitations of conventional topical therapies. Curcumin possesses potent anti-inflammatory and antimicrobial properties; however, its clinical application is hindered by poor solubility and stability. Nanotechnology-based, green synthesis approaches offer a promising strategy to overcome these limitations. This study aimed to develop and evaluate a thermosensitive curcumin–soya protein complex silver nanoparticle gel using a green synthesis approach for topical burn wound applications. Curcumin-loaded silver nanoparticles were synthesized using soy protein isolate as a bioreducing and stabilizing agent, avoiding toxic chemical reducers. The nanoparticles were characterized using ultraviolet–visible (UV–Vis) spectroscopy, X-ray diffraction (XRD), differential scanning calorimetry (DSC), Attenuated Total Reflectance–Fourier Transform Infrared (ATR–FTIR) spectroscopy, dynamic light scattering (DLS), zeta potential analysis, and scanning electron microscopy (SEM). The nanoparticles were incorporated into thermosensitive gel formulations, which were evaluated for physicochemical properties, in vitro drug release, release kinetics, and antibacterial activity. UV–Vis spectroscopy showed a characteristic surface plasmon resonance peak at approximately 424 nm, confirming silver nanoparticle formation. The nanoparticles exhibited an average size of 161.7 nm and a zeta potential of −16.2 mV. DSC analysis revealed a substantial reduction in curcumin crystallinity (~97%). The optimized gel displayed skin-compatible pH (4.9–5.5), high viscosity (1696 ± 10.79 cP), and drug content exceeding 92%. Sustained curcumin release of 85.32% over 24 h was observed, following diffusion-controlled Higuchi kinetics. The curcumin–silver nanoparticle gel demonstrated enhanced antibacterial activity against Staphylococcus aureus, with a zone of inhibition of approximately 9.4 mm. The green-synthesized thermosensitive curcumin–silver nanoparticle gel represents a promising in vitro platform for controlled topical delivery and antimicrobial activity in burn wound management, warranting further in vivo and clinical evaluation