Composite magnetoplasmonic nanoparticles with a core-shell morphology exhibit intriguing optical properties and offer impressive opportunities for tailoring in a controllable manner the light-matter interaction at subwavelength dimensions. These properties are usually analyzed in the framework of the quasi-static approximation, which, however, is often inadequate; thus, a full electrodynamic treatment is required. In this respect, we developed a rigorous method for an accurate description of electromagnetic scattering by a gyrotropic sphere coated with a nongyrotropic concentric spherical shell, based on the full multipole expansion of the wave field. The method was applied to specific examples of core-shell cobalt-silver spherical nanoparticles, where the occurrence of strong circular dichroism induced by magnetoplasmonic interaction, which largely exceeds that of homogeneous noble metal nanoparticles in an external magnetic field, was found. Our results were also explained by reference to the quasi-static approximation, which, though it reproduces the main features of the absorption spectra, strongly overestimates circular dichroism in the cases we studied.