The effective stiffness of materials that are impregnated with magnetic nanoparticles can be modulated by magnetic fields if the nanoparticle Neel relaxation rates are slower than the characteristic deformation rates. A numerical analysis indicates that the deflection of magnetic dipoles against the applied magnetic field on deformation of the material provides the energy absorption necessary for the enhanced stiffness observed in drop ball impact tests. The penetration depth, fraction of the impact energy that is absorbed by the rotating dipoles, and the effective increase in stiffness are shown to depend uniquely on the ratio of the characteristic magnetic energy density relative to the elastic energy density, and on the shape of the impacting object.