Hyperbolic nanoparticles provide a versatile platform to widely tune light-matter interactions. 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 response of hyperbolic nanoparticles across the visible and near infrared spectral range. By using a perturbative approach, we establish a model where the magneto-optical activity of the system is described in terms of the coupling of fundamental electric and magnetic dipole modes, which are induced by the hyperbolic dispersion, with a static magnetic field. Finally, an analytical model is established in the framework of Mie theory to describe the magneto-optical response and identify the contribution of electric and magnetic modes to the total spectrum.