Using first-principles calculations, we studied Mn\(_2\)RuZ (Z=Al, Ga, Si, Ge) and their heterojunctions with MgO along (001) direction. All these alloys possess Hg\(_2\)CuTi-type inverse Heusler alloy structure and ferrimagnetic ground state. Our study reveals the half-metallic electronic structure with highly spin-polarized \(\Delta_1\) band, which is robust against atomic disorder. Next we studied the electronic structure of Mn\(_2\)RuAl/MgO and Mn\(_2\)RuGe/MgO heterojunctions. We found that the MnAl- or MnGe-terminated interface is energetically more favorable compared to the MnRu-terminated interface. Interfacial states appear at the Fermi level in the minority-spin gap for the Mn\(_2\)RuGe/MgO junction. We discuss the origin of these interfacial states in terms of local environment around each constituent atom. On the other hand, in the Mn\(_2\)RuAl/MgO junction, high spin polarization of bulk Mn\(_2\)RuAl is preserved independent of its termination.