Geodetic observations of postseismic transients following earthquakes commonly help to inform the rheology of the lower crust and mantle, frictional properties of faults, and the kinematics of deformation across the earthquake cycle. Here we use interferometric synthetic aperture radar time series observations of postseismic deformation following the 2013 Mw 7.7 Baluchistan, Pakistan earthquake to investigate the viscoelastic rheology of the Makran accretionary prism. Using observations that began 15 months after the earthquake and a suite of potential fault geometries, we show that the ongoing deformation transient in the vicinity of the earthquake cannot be explained by afterslip alone. Instead, the gross spatial and temporal characteristics of the transient can be explained by viscoelastic relaxation of a shallow (>6 km) weak zone bounded by the Baluchistan earthquake and the underthrusting Arabian oceanic plate. Our first-order results show that the viscoelastic lower accretionary prism has a thickness of 8–12 km and exhibits power law (n = 3.5) behavior with viscosities of 1017–1018 Pa·s. These estimated viscosities may be higher if afterslip occurred during the initial period of postseismic deformation not constrained by our observations. The power law rheology suggests that creep processes common at lower crustal and mantle temperatures may be active at comparatively lower temperatures in the Makran. We hypothesize that the weak nature of the Makran accretionary prism is driven by high pore fluid pressures introduced by underplated sediments and/or hydrocarbon development, and we show a mechanically weak accretionary prism may lead to overestimates of plate coupling when linear elasticity is assumed. Plain Language Summary After earthquakes occur, surface deformation can continue in the surrounding region for several years. By modeling this deformation, we can make inferences about the properties of the Earth at depth in that region, such as the viscosity of the lower crust and mantle. In 2013, a large earthquake occurred in the Makran accretionary prism of southern Pakistan—a region of active plate subduction. We use satellite observations to measure the surface deformation after this earthquake and characterize the cause of this deformation—viscoelastic relaxation of the lower accretionary prism. We find that the lower Makran accretionary prism is surprisingly weak, with viscosities similar to those of the lower crust in Tibet and California. We show that a viscoelastic accretionary prism, in contrast to the classically defined elastic accretionary prism, may lead to overestimates of plate locking in subduction zone environments. Our findings thus hold important implications for the dynamics of the wedge, and regional earthquake and tsunami hazard assessment.