We show that an interlayer Dzyaloshinskii-Moriya interaction in combination with nonlocal damping gives rise to unidirectional magnetic coupling. That is, the coupling between two magnetic layers---say, the left and right layer---is such that the dynamics of the left layer leads to the dynamics of the right layer, but not vice versa. We discuss the implications of this result for the magnetic susceptibility of a magnetic bilayer, electrically actuated spin-current transmission, and unidirectional spin-wave packet generation and propagation. Our results may enable a route towards spin-current and spin-wave diodes and further pave the way to design spintronic devices via reservoir engineering.