Soil salinization is one of the main hazards affecting the sustainable development of agriculture in the Hetao Irrigation District (HID) of Inner Mongolia. To grasp the water and salt transport patterns and spatial–temporal distribution characteristics of the HID at the regional scale, the improved Soil and Water Assessment Tool with a salinity module (SWAT-Salt) model was used to establish the distributed water and salt transport model for the watershed in this study. The results demonstrated that the modified model could more accurately represent the process of water and salt changes in the HID. The coefficient of determination (R²) in the simulation of streamflow and discharge salt loading was 0.83 and 0.86, respectively, and the Nash–Sutcliffe efficiency (NSE) was 0.80 and 0.74, respectively. Based on this, different hydrological processes (surface runoff, lateral flow, groundwater, soil seepage) as well as spatial–temporal distribution characteristics of water salinity in groundwater and soil were analyzed in the HID. Differences in groundwater and soil salinity in different land uses and soil types were also compared. Of these, surface runoff and lateral flow salt discharge loading are concentrated in the southwestern portion of the basin, while groundwater salt discharge loading is concentrated in the eastern as well as southwestern portions of the basin. The salt discharge loading from groundwater accounts for about 98.7% of the total salt discharge loading from all hydrological pathways and is the major contributing part of salt discharge from the irrigation area. Soil salinity increases gradually from west to east. Groundwater salinity (2946 mg/L) and soil water electrical conductivity (0.309 dS/m) were minimized in the cropland. Meanwhile, rational allocation of irrigation water can appropriately increase the amount of salt discharge loading. In conclusion, the model could provide a reference for the investigation of soil salinization and water–salt management measures in irrigation areas.