Enceladus is a small icy satellite of Saturn. Its south polar region consists of young, tectonically deformed terrain and has an anomalously high heat flux. This heat flux is probably due to localized tidal dissipation within either the ice shell or the underlying silicate core. The surface deformation is plausibly due to upwelling of low-density material (diapirism) as a result of this tidal heating. Here we show that the current polar location of the hotspot can be explained by reorientation of the satellite's rotation axis because of the presence of a low-density diapir. If the diapir is in the ice shell, then the shell must be relatively thick and maintain significant rigidity (elastic thickness greater than approximately 0.5 km); if the diapir is in the silicate core, then Enceladus cannot possess a global subsurface ocean, because the core must be coupled to the overlying ice for reorientation to occur. The reorientation generates large (approximately 10 MPa) tectonic stress patterns that are compatible with the observed deformation of the south polar region. We predict that the distribution of impact craters on the surface will not show the usual leading hemisphere-trailing hemisphere asymmetry. A low-density diapir also yields a potentially observable negative gravity anomaly.