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Neutron diffraction and magnetic susceptibility studies of polycrystalline SrCr₂As₂ reveal that this compound is an itinerant G-type antiferromagnet below the Neel temperature T_N = 590(5) K with the Cr magnetic moments aligned along the tetragonal c axis. The system remains tetragonal to the lowest measured temperature (~12 K). The ordered moment, μ = 1.9(1) μ_B/Cr, measured at T = 12 K, is significantly reduced compared to its localized value (4 μ_B/Cr) due to the itinerant character brought about by hybridization between the Cr 3d and As 4p orbitals. Inelastic neutron scattering measurements on powder samples show steep columns of magnetic scattering arising from the magnetic Γ points, with the magnetic spectra persisting up to at least 150 meV. The spectra are modeled using a phenomenological J₁-J₂-J_c Heisenberg description with very large nearest- (J₁) and next-nearest-neighbor (J₂) AFM interactions within the square tetragonal basal plane and weak interlayer interactions (J_c).