Wetland vegetation aboveground biomass (AGB) directly indicates wetland ecosystem health and is critical for water purification, carbon cycle, and biodiversity conservation. Accurate AGB estimation is essential for the monitoring and supervision of ecosystems, especially in seasonal floodplain wetlands. This paper explored the capability of spectral and texture features from the Sentinel-2 Multispectral Instrument (MSI) for modeling grassland AGB using random forest (RF) and extreme gradient boosting (XGBoost) algorithms in Shengjin Lake wetland (a Ramsar site). We use five-fold cross-validation to verify the model effectiveness. The results indicated that the RF and XGBoost models had a robust and efficient performance (with root mean square error (RMSE) of 126.571 g·m−2 and R2 of 0.844 for RF, RMSE of 112.425 g·m−2 and R2 of 0.869 for XGBoost), and the XGBoost models, by contrast, performed better. Both traditional and red-edge vegetation indices (VIs) obtained satisfactory results of AGB estimation (RMSE = 127.936 g·m−2, RMSE = 125.879 g·m−2 in XGBoost models, respectively), with the red-edge VIs contributed more to the AGB models. Moreover, we selected eight gray-level co-occurrence matrix (GLCM) textures calculated by four processing window sizes using the mean value of four offsets, and further analyzed the results of three analysis sets. Textures derived from traditional and red-edge bands using a 7 × 7 window size performed better in biomass estimation. This finding suggested that textures derived from the traditional bands were as important as the red-edge bands. The introduction of textures moderately improved the accuracy of modeling AGB, whereas the use of textures alo ne was not satisfactory. This research demonstrated that using the Sentinel-2 MSI and the two ensemble algorithms is an effective method for long-term dynamic monitoring and assessment of grass AGB in seasonal floodplain wetlands, which can support sustainable management and carbon accounting of wetland ecosystems.