The Piton de la Fournaise basaltic volcano, on La Réunion Island in the western Indian Ocean, is one of the most active volcanoes in the world. This volcano is classically considered as the surface expression of an upwelling mantle plume and its activity is continuously monitored, providing detailed information on its superficial dynamics and on the edifice structure. Deeper crustal and upper mantle structure under La Réunion Island is surprisingly poorly constrained, motivating this study. We used receiver function techniques to determine a shear wave velocity profile through the crust and uppermost mantle beneath La Réunion, but also at other seismic stations located on the hotspot track, to investigate the plume and lithosphere interaction and its evolution through time. Receiver functions (RFs) were computed at permanent broad-band seismic stations from the GEOSCOPE network (on La Réunion and Rodrigues), at IRIS stations MRIV and DGAR installed on Mauritius and Diego Garcia islands, and at the GEOFON stations KAAM and HMDM on the Maldives. We performed non-linear inversions of RFs through modelling of P-to-S conversions at various crustal and upper mantle interfaces. Joint inversion of RF and surface wave dispersion data suggests a much deeper Mohorovičić discontinuity (Moho) beneath Mauritius (∼21 km) compared to La Réunion (∼12 km). A magmatic underplated body may be present under La Réunion as a thin layer (≤3 km thick), as suggested by a previous seismic refraction study, and as a much thicker layer beneath other stations located on the hotspot track, suggesting that underplating is an important process resulting from the plume–lithosphere interaction. We find evidence for a strikingly low velocity layer starting at about 33 km depth beneath La Réunion that we interpret as a zone of partial melt beneath the active volcano. We finally observe low velocities below 70 km beneath La Réunion and below 50 km beneath Mauritius that could represent the base of the oceanic lithosphere.