Abstract In the Aquistore deep saline CO2 storage project, researchers observed that most of the salt distribution is associated with perforations in a zone with low injectivity. However, the impact of salt precipitation in heterogeneous porous media has not been fully clarified. In this paper, we conducted laboratory experiments on subsurface cores from the Aquistore project to investigate the influence of heterogeneous porous structures with varying permeabilities on salt precipitation. The results show that due to capillary‐driven transport, salt precipitation primarily occurs at the front end of low‐permeability structures and within high‐permeability structures, consistent with observations in the Aquistore injector. We first found that salt precipitation within fracture led to self‐sealing of fracture. When CO2 was injected into a core containing horizontal fracture at a low flow rate, fracture closure was more likely to occur. Intermittent injection of low‐concentration brine was found to alleviate salt precipitation.