Nanoscale molecular-electronic devices and machines are emerging as promising functional elements, naturally flexible and efficient, for next-generation technologies. A deeper understanding of carrier dynamics in molecular junctions is expected to benefit many fields of nanoelectronics and power devices. We determine time-resolved charge current flowing at the donor-acceptor interface in molecular junctions connected to metallic electrodes by means of quantum transport simulations. The current is induced by the interaction of the donor with a Gaussian-shape femtosecond laser pulse. Effects of the molecular internal coupling, metal-molecule tunneling, and light-donor coupling on photocurrent are discussed. We then define the time-resolved local density of states which is proposed as an efficient tool to describe the absorbing molecule in contact with metallic electrodes. Non-equilibrium reorganization of hybridized molecular orbitals through the light-donor interaction gives rise to two phenomena: the dynamical Rabi shift and the appearance of Floquet-like states. Such insights into the dynamical photoelectronic structure of molecules are of strong interest for ultrafast spectroscopy and open avenues toward the possibility of analyzing and controlling the internal properties of quantum nanodevices with pump-push photocurrent spectroscopy.