Crop biomass is a critical variable to make sound decisions about field crop monitoring activities (fertilizers and irrigation) and crop productivity forecasts. More importantly, crop biomass estimations by components are essential for crop growth monitoring as the yield formation of crops results from the accumulation and transportation of substances between different organs. Retrieval of crop biomass from synthetic aperture radar SAR or optical imagery is of paramount importance for in-season monitoring of crop growth. A combination of optical and SAR imagery can compensate for their limitations and has exhibited comparative advantages in biomass estimation. Notably, the joint estimations of biophysical parameters might be more accurate than that of an individual parameter. Previous studies have attempted to use satellite imagery to estimate aboveground biomass, but the estimation of biomass for individual organs remains a challenge. Multi-target Gaussian process regressor stacking (MGPRS), as a new machine learning method, can be suitably utilized to estimate biomass components jointly from satellite imagery data, as the model does not require a large amount of data for training and can be adjusted to the required degrees of relationship exhibited by the given data. Thus, the aim of this study was to estimate the biomass of individual organs by using MGPRS in conjunction with optical (Sentinel-2A) and SAR (Sentinel-1A) imagery. Two hybrid indices, SAR and optical multiplication vegetation index (SOMVI) and SAR and optical difference vegetation index (SODVI), have been constructed to examine their estimation performance. The hybrid vegetation indices were used as input for the MGPRS and single-target Gaussian process regression (SGPR). The accuracy of the estimation methods was analyzed by in situ measurements of aboveground biomass (AGB) and organ biomass conducted in 2018 and 2019 over the paddy rice fields of Xinghua in Jiangsu Province, China. The results showed that the combined indices (SOMVI and SODVI) performed better than those derived from either the optical or SAR data only. The best predictive accuracy was achieved by the MGPRS using SODVI as input (r2 = 0.84, RMSE = 0.4 kg/m2 for stem biomass; r2 = 0.87, RMSE = 0.16 kg/m2 for AGB). This was higher than using SOMVI as input for the MGPRS (r2 = 0.71, RMSE = 1.12 kg/m2 for stem biomass; r2 = 0.71, RMSE = 0.56 kg/m2 for AGB) or SGPR (r2 = 0.63, RMSE = 1.08 kg/m2 for stem biomass; r2 = 0.67, RMSE = 1.08 kg/m2 for AGB). Relatively, higher accuracy for leaf biomass was achieved using SOMVI (r2 = 0.83) than using SODVI (r2 = 0.73) as input for MGPRS. Our results demonstrate that the combined indices are effective by integrating SAR and optical imagery and MGPRS outperformed SGPR with the same input variable for estimating rice crop biomass. The presented workflow will improve the estimation of crops biomass components from satellite data for effective crop growth monitoring.