We demonstrate that it is possible to localize photons nonreciprocally in a moving photonic lattice made by spatiotemporally modulating the atomic response, where the dispersion acquires a spectral Doppler shift with respect to the probe direction. A static defect placed in such a moving lattice produces a spatial localization of light in the band gap with a shifting frequency that depends on the direction of incident field with respect to the moving lattice. This phenomenon has an impact not only in photonics but also in broader areas such as condensed matter and acoustics, opening the doors for designing new devices such as compact isolators, circulators, nonreciprocal traps, sensors, unidirectional tunable filters, and possibly even a unidirectional laser.