Starting from the minimal model for the electrically interacting densities of electrons and ions in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. Solutions of the moving boundary model have already been discussed, but the derivation of the model was postponed to the present paper. The key ingredient of the model is the boundary condition on the moving front. It is found to be of kinetic undercooling type, and the relation to other moving boundary models is discussed. Furthermore, the model is compared to two-dimensional simulations of the underlying density model. The results suggest that our moving boundary approximation adequately represents the essential dynamics of negative streamer fronts.