<p>Out of equilibrium, the action-reaction symmetry of interactions is often broken, leading to the emergence of various collective phenomena with no equilibrium counterparts. Although ubiquitous in classical active systems, implementing such non-reciprocal interactions in solid-state systems has remained challenging, as known quantum schemes require precise single-site control. Here, we propose a dissipation-engineering protocol that induces non-reciprocal interactions in solid-state platforms with light, which we expect to be achievable with state-of-the-art experimental techniques. Focusing on magnetic metals, we show microscopically that a light injection that introduces a decay channel to a virtually excited state gives rise to non-reciprocal interactions between localized spins, resulting in chase-and-runaway dynamics. Applying our scheme to layered ferromagnets, we show that a non-reciprocal phase transition to a many-body time-dependent chiral phase occurs. Our work paves the way to bring solid-state systems to the realm of non-reciprocal science, providing yet another possibility to control quantum matter with light.</p>