We construct Vaidya-type solutions of quasitopological gravity coupled to nonlinear electrodynamics in arbitrary spacetime dimensions. Starting from the corresponding static spherically symmetric charged solutions, we obtain their dynamical counterparts by promoting the integration constants, in particular the mass and electric charge, to arbitrary functions of the advanced or retarded null coordinate. We show that the resulting field equations are satisfied provided suitable charge-carrying null currents and null fluid fluxes are included. The formalism applies to a broad class of nonlinear electromagnetic theories and provides a simple and systematic method for generating exact radiating charged solutions in quasitopological gravity.