ABSTRACT The Ly α emission line is one of the most promising probes of cosmic reionization but isolating the signature of a change in the ionization state of the intergalactic medium (IGM) is challenging because of intrinsic evolution and internal radiation transfer effects. We present the first study of the evolution of Ly α emitters (LAE) during the epoch of reionization based on a full radiation-hydrodynamics cosmological simulation that is able to capture both the large-scale process of reionization and the small-scale properties of galaxies. We predict the Ly α emission of galaxies in the 103 cMpc3sphinx simulation at 6 ≤ z ≤ 9 by computing the full Ly α radiation transfer from interstellar medium (ISM) to IGM scales. sphinx is able to reproduce many observational constraints such as the UV/Ly α luminosity functions and stellar mass functions at z ≳ 6 for the dynamical range probed by our simulation (M1500 ≳ −18, LLy α ≲ 1042 erg s−1, M⋆ ≲ 109 M⊙). As intrinsic Ly α emission and internal Ly α escape fractions barely evolve from z = 6–9, the observed suppression of Ly α luminosities with increasing redshift is fully attributed to IGM absorption. For most observable galaxies (M1500 ≲ −16), the Ly α line profiles are slightly shifted to the red due to internal radiative transfer effects that mitigates the effect of IGM absorption. Overall, the enhanced Ly α suppression during reionization traces the IGM neutral fraction $x_{{\rm H\, {i}}}$ well, but the predicted amplitude of this reduction is a strong function of the Ly α peak shift, which is set at ISM/circumgalactic medium scales. We find that a large number of LAEs could be detectable in very deep surveys during reionization when $x_{{\rm H\, {i}}}$ is still $\approx 50{{\ \rm per\ cent}}$.