To investigate the controls on continental rifting in the Western Branch of the East Africa Rift System, we conduct shear‐velocity imaging of the crust and uppermost mantle beneath the weakly extended Malawi Rift and the Rungwe Volcanic Province (RVP). We use local‐scale measurements of Rayleigh‐wave phase velocities between 9‐ and 100‐s period combined with constraints on basin architecture and crustal thickness to invert for shear velocity from the surface to ~135 km. Our resulting 3‐D model reveals a localized low‐velocity anomaly associated with the RVP extending from the crust and through the upper mantle, which can be explained with modestly elevated temperatures. Away from the RVP, velocities within mantle flanking the rift are fast (> 4.6±0.1 km/s), suggesting depleted lithospheric mantle to depths of ~100 km and >135 km to the west and east of the rift, respectively. The upper mantle beneath the rift axis is characterized by thinned lithosphere with slower velocities than the surrounding plateau, suggestive of thermal and/or chemical modification by the rifting process. Slowest velocities are mildly asymmetric about the rift axis, with the lowest velocities observed beneath the rift and adjacent footwall escarpments. The underlying asthenosphere is only moderately slow (~4.25±0.1 km/s), including beneath the RVP, precluding the presence of significant volumes of partial melt. The positions of localized lithospheric modification and basin‐bounding border faults correlate with the location of Proterozoic mobile belts, suggesting that these sutures provide lithospheric‐scale weakening mechanisms necessary for localizing strain and allowing extension to occur in the Malawi Rift.