We offer an explanation for the recently observed pressure-induced magnetic state in the iron-chalcogenide FeSe based on textit{ab initio} estimates for the pressure evolution of the most important Coulomb interaction parameters. We find that an increase of pressure leads to an overall decrease mostly in the nearest-neighbor Coulomb repulsion, which in turn leads to a reduction of the nematic order and the generation of magnetic stripe order. We treat the concomitant effects of band renormalization and the induced interplay of nematic and magnetic order in a self-consistent way and determine the generic topology of the temperature-pressure phase diagram, and find qualitative agreement with the experimentally determined phase diagram.
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