In the present contribution a localization analysis is performed for a two-scale dynamic damage model. The damage evolution law considered here results by homogenization from micro-crack propagation criteria and involve a characteristic length of the microstructure. For the one-dimensional dynamic system, we study the localization of strain and damage using analytical and numerical methods. An instability analysis based on harmonic perturbations of a homogeneous state for the linearized equations reveals wave dispersion properties and an intrinsic length of the model is deduced in the high frequency regime. The explicit dependence of this intrinsic length on the microstructural length and the damage level is obtained. Numerical simulations of dynamic tests illustrate the localization of damage, strain-rate sensitivity of the tensile strength and the influence of the size of the microstructure. The model predictions are compared with experimental results for spalling tests on concrete specimens. It is shown that the damage model is able to reproduce the observed influences of the strain rate and the size of the microstructure on the dynamic tensile strength.