Understanding the capillary imbibition laws of brackish water in rocks is necessary to reveal the mechanism of fluid, salt, and ion transport. In this study, we investigated the capillary imbibition laws of a Na2SO4 solution of different concentrations in sandstone by measuring the parameters of water absorption mass, water migration front height, nuclear magnetic resonance (NMR) T2 spectra, and stratified moisture distribution. The results indicate the following: (1) With an increase in the salt solution concentration, the water absorption rate of samples increases, specifically manifested in an increase in the rate of absorption mass and a rising rate of the absorption front. (2) With an increase in the salt solution concentration, the total NMR signals in samples measured at the end of water absorption decreases; that is, the total amount of water absorption decreases. (3) When the solution concentration exceeds 0.50 g/L, variations in the NMR signal of samples and the absorbed water mass over time are not synchronic and are even opposite at some stages. Based on the capillary dynamic theories of liquid, the influence of salts on solution properties and the modification of the pore structure by crystallization are considered when discussing the underlying mechanism of capillary imbibition in sandstone. By calculating the physical properties such as the density, viscosity, surface tension, and contact angle of solutions with different concentrations, the imbibition process does not exhibit any significant variation with the difference in the properties of the liquid. The equivalent capillary radii of the samples at varying salt concentrations are obtained by fitting the capillary dynamics curves with the theoretically calculated values. The equivalent capillary radii of samples in higher salt concentrations are larger, i.e., the difference in capillary imbibition laws introduced by the salt concentration should be attributed to modifications to the pore structure caused by salt crystallization.