Shear‐wave splitting measurements in the Galápagos archipelago show a rapid change from consistently oriented anisotropy to no measurable anisotropy. At the western edge of the archipelago delay times are 0.4–0.9 s and fast polarization directions are 81–109°E. These directions are consistent with anisotropy resulting from shear of the asthenosphere by the overlying plate; there is no indication of fossil lithospheric anisotropy in the plate spreading direction. In contrast, beneath the center of the archipelago the upper mantle is isotropic or weakly anisotropic. The isotropic region coincides approximately with a volume of anomalously low upper mantle velocities, suggesting that the presence of melt may weaken the effects of fabric on anisotropy or that melt preferred orientation generates a vertical fast polarization direction. Alternatively, the complex flow field associated with a near‐ridge hotspot may result in apparent isotropy.