Barite scalings are a common cause of permanent formation damage to deep geothermal reservoirs. Well injectivity can be impaired because the ooling of saline fluids reduces the solubility of barite, and the continuous re-injection of supersaturated fluids forces barite to precipitate in the host rock. Stimulated reservoirs in the Upper Rhine Graben often have multiple relevant flow paths in the porous matrix and fracture zones, sometimes spanning multiple stratigraphical units to achieve the economically necessary injectivity. While the influence of barite scaling on injectivity has been investigated for purely porous media, the role of fractures within reservoirs consisting of both fractured and porous sections is still not well understood. Here, we present hydro-chemical simulations of a dual-layer geothermal reservoir to study the long-term impact of barite scale formation on well injectivity. Our results show that, compared to purely porous reservoirs, fractured porous reservoirs have a significantly reduced scaling risk by up to 50%, depending on the flow rate ratio of fractures. Injectivity loss is doubled, however, if the amount of active fractures is increased by one order of magnitude, while the mean fracture aperture is decreased, provided the fractured aquifer dictates the injection rate. We conclude that fractured, and especially hydraulically stimulated, reservoirs are generally less affected by barite scaling and that large, but few, fractures are favourable. We present a scaling score for fractured-porous reservoirs, which is composed of easily derivable quantities such as the radial equilibrium length and precipitation potential. This score is suggested for use approximating the scaling potential and its impact on injectivity of a fractured-porous reservoir for geothermal exploitation.