The crust and upper mantle of the Madagascar continental fragment remained largely unexplored until a series of recent broadband seismic experiments. An island-wide deployment of broadband seismic instruments has allowed the first study of phase velocity variations, derived from surface waves, across the entire island. Late Cenozoic alkaline intraplate volcanism has occurred in three separate regions of Madagascar (north, central and southwest), with the north and central volcanism active until <1 Ma, but the sources of which remains uncertain. Combined analysis of three complementary surface wave methods (ambient noise, Rayleigh wave cross-correlations, and two-plane-wave) illuminate the upper mantle down to depths of 150 km. The phase-velocity measurements from the three methods for periods of 8-182 s are combined at each node and interpolated to generate the first 3-D shear-velocity model for sub-Madagascar velocity structure. Shallow (upper 10 km) low-shear-velocity regions correlate well with sedimentary basins along the west coast. Upper mantle low-shear-velocity zones that extend to at least 150 km deep underlie the north and central regions of recent alkali magmatism. These anomalies appear distinct at depths <100 km, suggesting that any connection between the zones lies at depths greater than the resolution of surface-wave tomography. An additional low-shear velocity anomaly is also identified at depths 50-150 km beneath the southwest region of intraplate volcanism. We interpret these three low velocity regions as upwelling asthenosphere beneath the island, producing high-elevation topography and relatively low-volume magmatism.