Inner solar system bodies, including the Earth, Moon, and asteroids, are depleted in volatile elements relative to chondrites. Hypotheses for this volatile element depletion include condensation from the solar nebula and volatile loss during energetic impacts. These processes are expected to each produce characteristic stable isotope signatures. However, processes of planetary differentiation may also modify the isotopic composition of geochemical reservoirs. Angrites are rare meteorites that only a few million years after calcium-aluminum-rich inclusions and exhibit extreme depletions in volatile elements relative to chondrites, making them ideal samples with which to study volatile element depletion in the early solar system. Here we present high-precision Si isotope data that show angrites are enriched in the heavy isotopes of Si relative to chondritic meteorites by 50-100 ppm/amu. Silicon is sufficiently volatile such that it may be isotopically fractionated during incomplete condensation or evaporative mass loss, but theoretical calculations and experimental results also predict isotope fractionation under specific conditions of metal-silicate differentiation. We show that the Si isotope composition of angrites cannot be explained by any plausible core formation scenario, but rather reflects isotope fractionation during impact-induced evaporation. Our results indicate planetesimals initially formed from volatile-rich material and were subsequently depleted in volatile elements during accretion.