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Formation dry‐out in fracture‐dominated geological reservoirs may alter the fracture space, impair rock absolute permeability and cause a significant decrease in well injectivity. In this study, we numerically model the dry‐out processes occurring during supercritical CO₂ (scCO₂) injection into single brine‐filled fractures and evaluate the potential for salt precipitation under increasing effective normal stresses in the evaporative regime. We use an open‐source, parallel finite‐element framework to numerically model two‐phase flow through 2‐Dimensional fracture planes with aperture fields taken from naturally fractured granite cores at the Grimsel Test Site in Switzerland. Our results reveal a displacement front and a subsequent dry‐out front in all simulated scenarios, where higher effective stresses caused more flow channeling, higher rates of water evaporation and larger volumes of salt precipitates. However, despite the larger salt volumes, the permeability impairment was lower at higher effective normal stresses. We conclude that the spatial distribution of the salt, precipitated in fractures with heterogeneous aperture fields, strongly affects the absolute permeability impairment caused by formation dry‐out. The numerical simulations assist in understanding the behavior of the injectivity in fractures and fracture networks during subsurface applications that involve scCO₂ injection into brine.