An accurate and efficient estimation of eucalyptus plantation areas is of paramount significance for forestry resource management and ecological environment monitoring. Currently, combining multidimensional optical and SAR images with machine learning has become an important method for eucalyptus plantation classification, but there are still some challenges in feature selection. This study proposes a feature selection method that combines multi-temporal Sentinel-1 and Sentinel-2 data with SLPSO (social learning particle swarm optimization) and RFE (Recursive Feature Elimination), which reduces the impact of information redundancy and improves classification accuracy. Specifically, this paper first fuses multi-temporal Sentinel-1 and Sentinel-2 data, and then carries out feature selection by combining SLPSO and RFE to mitigate the effects of information redundancy. Next, based on features such as the spectrum, red-edge indices, texture characteristics, vegetation indices, and backscatter coefficients, the study employs the Simple Non-Iterative Clustering (SNIC) object-oriented method and three different types of machine-learning models: Random Forest (RF), Classification and Regression Trees (CART), and Support Vector Machines (SVM) for the extraction of eucalyptus plantation areas. Each model uses a supervised-learning method, with labeled training data guiding the classification of eucalyptus plantation regions. Lastly, to validate the efficacy of selecting multi-temporal data and the performance of the SLPSO–RFE model in classification, a comparative analysis is undertaken against the classification results derived from single-temporal data and the ReliefF–RFE feature selection scheme. The findings reveal that employing SLPSO–RFE for feature selection significantly elevates the classification precision of eucalyptus plantations across all three classifiers. The overall accuracy rates were noted at 95.48% for SVM, 96% for CART, and 97.97% for RF. When contrasted with classification outcomes from multi-temporal data and ReliefF–RFE, the overall accuracy for the trio of models saw an increase of 10%, 8%, and 8.54%, respectively. The accuracy enhancement was even more pronounced when juxtaposed with results from single-temporal data and ReliefF-RFE, at increments of 15.25%, 13.58%, and 14.54% respectively. The insights from this research carry profound theoretical implications and practical applications, particularly in identifying and extracting eucalyptus plantations leveraging multi-temporal data and feature selection.