Active nanophotonics can be realized by controlling the optical properties of materials with external magnetic fields. Here, we explore the influence of optical anisotropy on the magneto-optical activity in nonmagnetic hyperbolic nanoparticles. We demonstrate that the magneto-optical response is driven by the hyperbolic dispersion via the coupling of metallic-induced electric and dielectric-induced magnetic dipolar optical modes with static magnetic fields. Magnetic circular dichroism experiments confirm the theoretical predictions and reveal tunable magneto-optical activity across the visible and near infrared spectral range.