Magnetoplasmons are the coupling of an external magnetic field and a plasmon or a localized plasmon, in the case of nanoparticles. We present a theoretical study, in the quasi-static limit, of the plasmonic response of nanoparticles when a constant magnetic field is applied. The plasmonic modes split into two satellite peaks with a frequency shift proportional to the magnetic field. The constant of proportionality is the effective Bohr magneton. This splitting of the fundamental plasmonic mode is akin to the splitting of energy levels in the Zeeman effect. The results are valid for any material that has a plasmonic response. For higher magnetic fields, the frequency shift of the splitting becomes non-linear with the magnetic field as what happens with the non-linear Zeeman effect.