Optical diodes controlling the flow of light are of principal significance for optical information processing. They transmit light from an input to an output, but not in the reverse direction. This breaking of time reversal symmetry is conventionally achieved via Faraday or nonlinear effects. For applications in a quantum network, features such as the abilities of all-optical control, on-chip integration, and single-photon operation are important. Here we propose an all-optical optical diode which requires neither magnetic fields nor strong input fields. It is based on a “moving” photonic crystal generated in a three-level electromagnetically induced transparency medium in which the refractive index of a weak probe is modulated by the moving periodic intensity of a strong standing coupling field with two detuned counterpropagating components. Because of the Doppler effect, the frequency range of the crystal’s band gap for the probe copropagating with the moving crystal is shifted from that for the counterpropagating probe. This mechanism is experimentally demonstrated in a room temperature Cs vapor cell.