Recently, inorganic metal halide perovskites, APbI₃ (A = K, Rb, and Cs), have attracted increased attention in the research community of photovoltaic technology due to their superior stability and exceptional structural, electronic, and optical properties. In this paper, the influence of biaxial compressive and tensile strains (−6% to +6%) on the optoelectronic properties of APbI₃ perovskites is thoroughly investigated using density functional theory, based on first-principles calculations. Additionally, this study identifies the function of the A-cation in the optoelectronic properties of APbI₃. We find that the biaxial strain in APbI₃ can significantly increase its absorbance, both in the visible and ultraviolet light energy range. Interestingly, the absorption coefficient, dielectric function, and electron loss function are tuned into visible ranges when a compressive strain is applied, whereas these functions move into the ultraviolet region for tensile strain. Furthermore, the electronic band structure shows that the APbI₃ compounds are all semiconductors with direct bandgap ranges of 0.92–1.09 eV and 1.9 eV at the R-point. The value of the bandgap decreases to 0.17, 0.25, and 0.32 eV for KPbI₃, RbPbI₃, and CsPbI₃, respectively, when the spin–orbit coupling effect is considered. Moreover, the bandgap of APbI₃ shows a decreasing trend and tends towards the metallic condition when compressive strain is applied. In addition, when tensile strain is increased, the bandgap of APbI₃ exhibits an increasing trend. Therefore, based on the optical and electronic properties, applying a biaxial strain should make APbI₃ compounds suitable for optoelectronic device applications.