Jupiter’s volcanic moon Io possesses some of the highest relief in the Solar System: massive, isolated mountain blocks that tower up to 17 km above the surrounding plains. These mountains are likely to result from pervasive compressive stresses induced by subsidence of the surface beneath the near-continual emplacement of volcanic material. The stress state that results from subsidence and warming of Io’s lithosphere has been investigated in detail^{1, 2, 3, 4}; however, the mechanism of orogenesis itself and its effect on regional tectonism and volcanism has not been firmly established. Here we present viscoelastic–plastic finite element simulations demonstrating that Io’s mountains form along deep-seated thrust faults that initiate at the base of the lithosphere and propagate upward. We show that faulting fundamentally alters the stress state of Io’s lithosphere by relieving the large volcanism-induced subsidence stresses. Notably, in the upper portion of the lithosphere, stresses become tensile (near-zero differential stress). A number of processes are therefore altered post-faulting, including magma transport through the lithosphere, interactions with tidal stresses and potentially the localization of mountain formation by thermoelastic stresses. We conclude that Io’s mountains form by a unique orogenic mechanism, compared with tectonic processes operating elsewhere in the Solar System.