The extreme case of an Fe monolayer deposited onto a manganese arsenide (MnAs) substrate is analyzed using density functional theory. We find that an FeAs quasi-two-dimensional antiferromagnetic surface nanostructure emerges. This nanostructure, which is magnetically nearly decoupled from the substrate, is due to bonding effects arising from the arsenic atoms bridging the Fe magnetic interactions. These interactions are studied and modeled using a Heisenberg-type Hamiltonian. They display an angular dependence which is characteristic of superexchange-like interactions, which are of the same order of magnitude as those appearing in Fe-based pnictides.