We present a theoretical study of the effect of an external dc magnetic field in the near-field radiative heat transfer between two one-dimensional magneto-photonic crystals with unit cells comprising a magneto-optical layer made of n-doped InSb and a dielectric layer. We find that in absence of an external field, and depending on the gap size, the radiative heat transfer between these multilayer structures can be larger or smaller than that of the case of two InSb infinite plates. On the other hand, when an external magnetic field is applied, the near-field radiative heat transfer is reduced as a consequence of the suppression of hybridized surface polariton waves that are supported for transverse magnetic polarized light. We show that such reduction is exclusively due to the appearance of magnetic-field induced hyperbolic modes, and not to the polarization conversion in this magneto-optical system.