Melting of the mantle during continental breakup leads to magmatic intrusion and volcanism, yet our understanding of the location and dominant mechanisms of melt generation in rifting environments is impeded by a paucity of direct observations of mantle melting. It is unclear when during the rifting process the segmented nature of magma supply typical of seafloor spreading initiates. Here, we use Rayleigh-wave tomography to construct a high-resolution absolute three-dimensional shear-wave velocity model of the upper 250 km beneath the Afar triple junction, imaging the mantle response during progressive continental breakup. Our model suggests melt production is highest and melting depths deepest early during continental breakup. Elevated melt production during continental rifting is likely due to localized thinning and melt focusing when the rift is narrow. In addition, we interpret segmented zones of melt supply beneath the rift, suggesting that buoyancy-driven active upwelling of the mantle initiates early during continental rifting.