Ab initio study of electronic structure and magnetism of graphene monolayer doped by the MnF2 molecule was performed based on the density functional theory. Functionalized graphene of the MnF2/SLG type is placed on the polar surface (1 1 1) of manganese monoxide, terminated by oxygen (with variable number of vacancies) or manganese in the MnF2/SLG/MnO (1 1 1) interface. Local atomic reconstruction of the functionalized graphene and MnO (1 1 1) interface were analyzed, the bond lengths were determined. The effects of graphene adsorption on electronic spectrum and magnetism in heterostructure of MnF2/SLG/MnO (1 1 1) were found for its different reconstructions. Effective charges and local magnetic moments on carbon atoms and the nearest-neighbor atoms were determined for the considered configurations. The charge transfer on carbon atoms from nearest-neighbor atoms was found due to the reconstruction of the local atomic and electronic structures. This paper predicts the magnetism of functionalized graphene placed on the polar surface of the MnO (1 1 1) insulator. The effects of the local magnetic moments on near-surface layer manganese atoms and the adsorbed MnF2 molecule on magnetism induction in graphene are discussed.