The asymptotic behavior of the equilibrium radiation in Maxwellian plasma is investigated for the region of low frequencies. It is shown, that already for a weakly non-ideal plasma the equilibrium radiation can essentially deviate from the Planck law. The deviation from the Planck distribution is described by the transverse dielectric permittivity which takes into account both frequency and spatial dispersion. The influence of plasma non-ideality increases with increase of the non-ideality parameter in the dielectric permittivity. The spectral energy distribution of the equilibrium radiation essentially changes in the region of possibly observable frequencies. At asymptotically low frequencies there is transfer from logarithmic to power behavior of the equilibrium radiation. The results indicate that in the primordial plasma of Early Universe the spectral energy distribution of radiation could be different than the Planck one.