We study impurity-induced magnetic order within a five-band Hubbard model relevant to the normal paramagnetic phase of iron-based superconductors. The existence of the local magnetic order is explained in terms of an impurity-enhancement of states near the Fermi level, and we map out the resulting phase diagram of the existence of magnetization as a function of impurity strength and Coulomb correlations. In particular, the presence of impurity-induced magnetism in only a certain range of potential scattering strengths can be understood from the specific behavior of the impurity resonant state.