We theoretically demonstrate the nonreciprocal behavior, for circularly polarized electromagnetic waves, of a 2D cross-grating made of nano-slits filled with a gyrotropic material subject to an external polar bias magnetic field. We provide closed-form expressions for the reflection and transmission of the system, allowing one to fully describe and understand the extraordinary optical transmission (EOT) mechanism occurring in the system. When the slits are filled with a gyrotropic material, the structure exhibits a non-reciprocal unidirectional light transmission in the EOT frequency range, which is fully explained by the proposed modal analytic analysis.