[en] We show that an appropriate description of the non-equilibrium dynamics of disordered systems is obtained through a strong disorder renormalization procedure in configuration space that we define for any master equation with transitions rates W(C→C') between configurations. The idea is to eliminate iteratively the configuration with the highest exit rate W_out(C)+Σ_C'W(C→C') to obtain renormalized transition rates between the remaining configurations. The multiplicative structure of the new generated transition rates suggests that for a very broad class of disordered systems, the distribution of renormalized exit barriers defined as B_out(C)≡-ln W_out(C) will become broader and broader upon iteration, so that the strong disorder renormalization procedure should become asymptotically exact at large time scales. We have checked numerically this scenario for the non-equilibrium dynamics of a directed polymer in a two-dimensional random medium