Radio relics are Mpc-scale diffuse radio sources at the peripheries of galaxy clusters which are thought to trace outgoing merger shocks. We present XMM-Newton and Suzaku observations of the galaxy cluster Abell 2744 (z = 0.306), which reveal the presence of a shock front 1.5 Mpc east of the cluster core. The surface-brightness jump coincides with the position of a known radio relic. Although the surface-brightness jump indicates a weak shock with aMach number M = 1.7(-0.3)(+0.5), the plasma in the post-shock region has been heated to a very high temperature (similar to 13 keV) by the passage of the shock wave. The low-acceleration efficiency expected from such a weak shock suggests that mildly relativistic electrons have been re-accelerated by the passage of the shock front.