Nanoparticle plasmon resonances can be controlled using external magnetic fields or internal magnetization. The modified resonance condition is complicated, however, by the induced anisotropy of the dielectric response. Working within the electrostatic regime, we formulate a simple eigenvalue problem for the magnetoplasmon resonances. Subsequently, a semianalytical perturbative solution valid for weak magnetic fields is obtained for the resonance shift. We apply the approach to Drude metal nanodisks and show that resonance shifts are generally smaller than for nanospheres and nanoellipsoids. Finally, energy-dependent effective masses in Dirac materials are shown to reduce shifts compared to free-electron-like materials.