All-inorganic halide perovskites have attracted significant interest in photodetector applications due to their remarkable photoresponse properties. However, the toxicity and instability of lead-based perovskites hinder their commercialization. In this work, we propose cubic Ba₃SbI₃ as a promising, environmentally friendly, lead-free material for next-generation photodetector applications. Ba₃SbI₃ shows good light absorption, low effective masses, and favorable elemental abundance and cost, making it a promising candidate compound for device applications. Its structural, mechanical, electronic, and optical properties were systematically investigated using density functional theory (DFT) with the Perdew–Burke–Ernzerhof (PBE) and hybrid HSE06 functionals. The material was found to be dynamically and mechanically stable, with a direct bandgap of 0.78 eV (PBE) and 1.602 eV (HSE06). Photodetector performance was then simulated in an Al/FTO/In₂S₃/Ba₃SbI₃/Sb₂S₃/Ni configuration using SCAPS-1D. To optimize device efficiency, the width, dopant level, and bulk concentration for each layer of the gadgets were systematically modified, while the effects of interface defects, operating temperature, and series and shunt resistances were also evaluated. The optimized device achieved an open-circuit voltage (Voc) of 1.047 V, short-circuit current density (Jsc) of 31.65 mA/cm², responsivity of 0.605 A W⁻¹, and detectivity of 1.05 × 10¹⁷ Jones. In contrast, in the absence of the Sb₂S₃ layer, the performance was reduced to a Voc of 0.83 V, Jsc of 26.8 mA/cm², responsivity of 0.51 A W⁻¹, and detectivity of 1.5 × 10¹⁵ Jones. These results highlight Ba₃SbI₃ as a promising platform for high-performance, cost-effective, and environmentally benign photodetectors.