Research on time crystals concerns the spontaneous breaking of translational symmetry in time, as well as the realization of phenomena and phases known from solid-state physics in the time domain. Periodically driven systems of massive particles are widely used in these studies. In the present work, we consider a photonic system and demonstrate that stable nonlinear propagation of a strong optical wave in a fiber with the third-order dispersion may lead to the establishment of quasi-periodic oscillations in the electromagnetic field intensity. A second, weaker signal optical wave propagating in the fiber senses these oscillations and, as a result, undergoes exponential localization in time. This is a temporal analog of Aubry–André localization. If an optical detector is placed at a certain position in the fiber, the temporal localization of the probe wave will be observed in the form of the signal which emerges and then decays as a function of time.