Studies of photoemission processes induced by hard X-rays including production of energetic electrons have become feasible due to recent substantial improvement of instrumentation. Novel dynamical phenomena have become possible to investigate in this new regime. Here we show a significant change in Auger emission following 1s photoionization of neon, which we attribute to the recoil of the Ne ion induced by the emission of a fast photoelectron. Because of the preferential motion of the ionized Ne atoms along two opposite directions, an Auger Doppler shift is revealed, which manifests itself as a gradual broadening and doubling of the Auger spectral features. This Auger Doppler effect should be a general phenomenon in high-energy photoemission of both isolated atoms and molecules, which will have to be taken into account in studies of other recoil effects such as vibrational or rotational recoil in molecules, and may also have consequences in measurements in solids.