Hyperspectral technology is widely recognized as an effective method for monitoring soil salinity. However, the traditional sieved samples often cannot reflect the true condition of the soil surface. In particular, there is a lack of research on the spectral response of cracked salt-affected soils despite the common occurrence of cohesive saline soil shrinkage and cracking during water evaporation. To address this research, a laboratory was designed to simulate the desiccation cracking progress of 57 soda saline–alkali soil samples with different salinity levels in the Songnen Plain of China. After completion of the drying process, spectroscopic analysis was conducted on the surface of all the cracked soil samples. Moreover, this study aimed to evaluate the predictive ability of multiple linear regression models (MLR) for four main salt parameters. The hyperspectral reflectance data was analyzed using three different band screening methods, namely random forest (RF), principal component analysis (PCA), and Pearson correlation analysis (R). The findings revealed a significant correlation between desiccation cracking and soil salinity, suggesting that salinity is the primary factor influencing surface cracking of saline–alkali soil in the Songnen Plain. The results of the modeling analysis also indicated that, regardless of the spectral dimensionality reduction method employed, salinity exhibited the highest prediction accuracy for soil salinity, followed by electrical conductivity (EC) and sodium (Na+), while the pH model exhibited the weakest predictive performance. In addition, the usage of RF for band selection has the best effect compared with PCA and Pearson methods, which allows salt information of soda saline–alkali soils in Songnen Plain to be predicted precisely.