The northward extent of subducted Indian plate is a fundamental component of hypotheses explaining deformation and magmatism within the Tibetan Plateau. Yet, these aspects of the plate are debated in west Tibet. Here we report a new three‐dimensional lithospheric structure of seismic velocity and radial anisotropy under west Tibet constructed from Rayleigh and Love wave phase velocity maps at periods of 20–167 and 20–125 s, respectively. Our results show the Indian lithospheric mantle to be subhorizontally subducted under west Tibet across the Bangong‐Nujiang suture to the Qiangtang terrane, as indicated by a prominent fast velocity anomaly accompanied with positive radial anisotropy (Vsh > Vsv). We find a positive spatial correlation of this result with information on the distribution of late Cenozoic potassic‐adakitic rocks in western Tibet. Additionally, we show that the midcrust of west Tibet is characterized by an anomalously low shear wave velocity (3.2–3.4 km/s at ~30‐km depth) and positive anisotropy, which is consistent with an estimated ~3% fraction of partial melt. We suggest that the midcrust of this region is capable of flowing and that its three‐dimensional structure shows it to extend south of the Karakoram fault (KKF), a shear zone interpreted as a barrier to crustal flow. Instead, our results are consistent with the KKF embedded in weak middle crust along with several other structures that display a pattern of distributed deformation in the western portion of the Tibetan Plateau.