We report ion acceleration by flux transfer events in the terrestrial magnetosheath in a global two‐dimensional hybrid‐Vlasov polar plane simulation of Earth's solar wind interaction. In the model we find that propagating flux transfer events created in magnetic reconnection at the dayside magnetopause drive fast‐mode bow waves in the magnetosheath, which accelerate ions in the shocked solar wind flow. The acceleration at the bow waves is caused by a shock drift‐like acceleration process under stationary solar wind and interplanetary magnetic field upstream conditions. Thus, the energization is not externally driven but results from plasma dynamics within the magnetosheath. Energetic proton populations reach the energy of 30 keV, and their velocity distributions resemble time‐energy dispersive ion injections observed by the Cluster spacecraft in the magnetosheath.