Understanding the crustal structure and the storage and movement of fluids beneath a volcano is necessary for characterising volcanic hazard, geothermal prospects and potential mineral resources. This study uses local earthquake traveltime tomography to image the seismic velocity structure beneath Nabro, an off-rift volcano located within the central part of the Danakil microplate near the Ethiopia-Eritrea border. Nabro underwent its first historically-documented eruption in June 2011, thereby providing an opportunity to analyse its post-eruptive state by mapping subsurface fluid distributions. We use a catalogue of earthquakes detected using machine learning methods to simultaneously relocate the seismicity and invert for the three-dimensional P- and S-wave velocity structures (Vp, Vs) and the ratio between them (Vp/Vs). Overall, our model shows higher than average P- and S-wave velocities, suggesting the presence of older consolidated volcanic deposits or intrusive magmatic rocks in the crust. We identify an aseismic region of low Vp, low Vs and high Vp/Vs ratio at depths of 6–10 km b.s.l., interpreted as the primary melt storage region that fed the 2011 eruption. Above this is a zone of high Vs, low Vp and low Vp/Vs ratio, representing an intrusive complex of fractured rocks partially-saturated with over-pressurised gases. Our observations identify the persistence of magma in the subsurface following the eruption, and track the degassing of this melt through the crust to the surface. The presence of volatiles and high temperatures within the shallow crust indicate that Nabro is a viable candidate for geothermal exploration.