Efficient acquisition of crop leaf moisture information holds significant importance for agricultural production. This information provides farmers with accurate data foundations, enabling them to implement timely and effective irrigation management strategies, thereby maximizing crop growth efficiency and yield. In this study, unmanned aerial vehicle (UAV) multispectral technology was employed. Through two consecutive years of field experiments (2021–2022), soybean (Glycine max L.) leaf moisture data and corresponding UAV multispectral images were collected. Vegetation indices, canopy texture features, and randomly extracted texture indices in combination, which exhibited strong correlations with previous studies and crop parameters, were established. By analyzing the correlation between these parameters and soybean leaf moisture, parameters with significantly correlated coefficients (p < 0.05) were selected as input variables for the model (combination 1: vegetation indices; combination 2: texture features; combination 3: randomly extracted texture indices in combination; combination 4: combination of vegetation indices, texture features, and randomly extracted texture indices). Subsequently, extreme learning machine (ELM), extreme gradient boosting (XGBoost), and back propagation neural network (BPNN) were utilized to model the leaf moisture content. The results indicated that most vegetation indices exhibited higher correlation coefficients with soybean leaf moisture compared with texture features, while randomly extracted texture indices could enhance the correlation with soybean leaf moisture to some extent. RDTI, the random combination texture index, showed the highest correlation coefficient with leaf moisture at 0.683, with the texture combination being Variance1 and Correlation5. When combination 4 (combination of vegetation indices, texture features, and randomly extracted texture indices) was utilized as the input and the XGBoost model was employed for soybean leaf moisture monitoring, the highest level was achieved in this study. The coefficient of determination (R2) of the estimation model validation set reached 0.816, with a root-mean-square error (RMSE) of 1.404 and a mean relative error (MRE) of 1.934%. This study provides a foundation for UAV multispectral monitoring of soybean leaf moisture, offering valuable insights for rapid assessment of crop growth.