This study focuses on theoretical and numerical investigations of the magnetochiral (MCh) effect in the optical region. Electrodynamics in a medium with broken time and space inversions is described by two orthogonal coupled oscillators, in what is known as the Born-Kuhn model, subject to an external static magnetic field. Constitutive equations and the refractive index of the medium are theoretically derived. The results show that the MCh effect is induced even in the absence of an intrinsic interaction between the magneto-optical effect and the optical activity. The study also numerically investigates the electromagnetic response in a metamaterial with magnetism and chirality in the deep ultraviolet region. The results agree well with the main results of our theory. This paper paves the way to realizing MCh metamaterials in the optical region.