Spitzer spectral maps reveal a disk of highly luminous, warm (>150 K) H2 in the center of the massive spiral galaxy Messier 58, which hosts a radio-loud active galactic nucleus (AGN). The inner 2.6 kpc of the galaxy appears to be overrun by shocks from the radio jet cocoon. Gemini NIRI imaging of the H2 1–0 S(1) emission line, Atacama Large Millimeter/submillimeter Array CO 2–1, and Hubble Space Telescope multiband imagery indicate that much of the molecular gas is shocked in situ, corresponding to lanes of dusty molecular gas that spiral toward the galactic nucleus. The CO 2–1 and ionized gas kinematics are highly disturbed, with velocity dispersion up to 300 km s‑1. Dissipation of the associated kinetic energy and turbulence, likely injected into the interstellar medium by radio-jet-driven outflows, may power the observed molecular and ionized gas emission from the inner disk. The polycyclic aromatic hydrocarbon (PAH) fraction and composition in the inner disk appear to be normal, in spite of the jet and AGN activity. The PAH ratios are consistent with excitation by the interstellar radiation field from old stars in the bulge, with no contribution from star formation. The phenomenon of jet-shocked H2 may substantially reduce star formation and help to regulate the stellar mass of the inner disk and supermassive black hole in this otherwise normal spiral galaxy. Similarly strong H2 emission is found at the centers of several nearby spiral and lenticular galaxies with massive bulges and radio-loud AGNs.