We study an interacting electron gas parabolically confined to a quantum wire in a perpendicular magnetic field. We consider the case of more than one subband occupied in the ground state. The intersubband spin-density excitations are calculated within the Hartree-Fock random-phase approximation. Similarly to the case in the absence of a magnetic field, vertex corrections to the electron spin polarizability are important, leading to collective spin-density excitations red-shifted with respect to the Hartree-Fock single-particle energies. In a finite magnetic field, the triplet of spin-density excitations splits. The splitting is at its maximum if the chemical potential is in between the bottom of a spin-up subband and the bottom of a spin-down subband, when the g-factor is greatly enhanced due to the exchange interaction.