We employed the relativistic configuration interaction plus second-order many-body perturbation theory (RCI+MBPT) method to calculate the energy levels, wave functions, and electric-dipole transition matrix elements for the ⁸⁷Sr atom. Within the sum-over-states framework, we systematically evaluated both static and dynamic electric-dipole polarizabilities for the ground-state 5s^{2 1}S₀ and the metastable clock state 5s5p ³P₀ under the fine level approximation. We compare our calculated fine-structure energy levels, reduced matrix elements, static polarizabilities, magic-zero wavelengths, and magic wavelengths with available theoretical and experimental data, and good agreement is achieved.
Subsequently, both magnetic dipole and electric quadrupole hyperfine interaction effects are incorporated. This allows us to obtain hyperfinesublevel-resolved polarizabilities, hyperfine-shifted magic-zero wavelengths for the two target states, and hyperfine-dependent magic wavelengths for the 5s^{2 1}S₀→5s5p ³P₀ clock transition. Our calculations confirm that hyperfine coupling induces non-vanishing tensor polarizabilities for both states. The hyperfine corrections to static and dynamic polarizabilities are on the order of 10^-4 a.u.. Due to hyperfine interactions, the magic-zero wavelengths of these two states change by about 10^-3-10^-4 nm. For the well-known 814-nm magic wavelength of the clock transition, the largest hyperfine-induced shift is about 10^-3 nm.