We investigate the influence of radiative transport on the growth of themagnetorotational instability (MRI) in accretion discs. A general dispersion relationdescribing the growth of small disturbances on a homogeneous background shear flow isprovided. It includes compressibility and radiative effects in the flux-limited diffusionapproximation. All the effects of radiation transport can be subsumed into one singleparameter, an effective speed of sound. Radiative diffusion does not affect the regionwhere the MRI operates, but it alters the growth rates of the MRI either by increasing ordecreasing them. We report about corresponding numerical simulations, which are also usedfor a first investigation of the non-linear stage of the MRI in gas-pressure dominatedaccretion discs with radiation transport included.