Rubber (Hevea brasiliensis Muell.) plantations are vital agricultural ecosystems in tropical regions. These plantations provide key industrial raw materials and sequester large amounts of carbon dioxide, playing a vital role in the global carbon cycle. Climate change has intensified droughts in Southeast Asia, negatively affecting rubber plantation growth. Limited in situ observations and short monitoring periods hinder accurate assessment of drought impacts on the gross primary productivity (GPP) of rubber plantations. This study used GPP data from flux observations at four rubber plantation sites in China and Thailand, along with solar-induced chlorophyll fluorescence (SIF), enhanced vegetation index (EVI), normalized difference vegetation index (NDVI), near-infrared reflectance of vegetation (NIRv), and photosynthetically active radiation (PAR) indices, to develop a robust GPP estimation model. The model reconstructed eight-day interval GPP data from 2001 to 2020 for the four sites. Finally, the study analyzed the seasonal drought impacts on GPP in these four regions. The results indicate that the GPP prediction model developed using SIF, EVI, NDVI, NIRv, and PAR has high accuracy and robustness. The model’s predictions have a relative root mean square error (rRMSE) of 0.22 compared to flux-observed GPP, with smaller errors in annual GPP predictions than the MOD17A3HGF model, thereby better reflecting the interannual variability in the GPP of rubber plantations. Drought significantly affects rubber plantation GPP, with impacts varying by region and season. In China and northern Thailand (NR site), short-term (3 months) and long-term (12 months) droughts during cool and warm dry seasons cause GPP declines of 4% to 29%. Other influencing factors may alleviate or offset GPP reductions caused by drought. During the rainy season across all four regions and the cool dry season with adequate rainfall in southern Thailand (SR site), mild droughts have negligible effects on GPP and may even slightly increase GPP values due to enhanced PAR. Overall, the study shows that drought significantly impacts rubber the GPP of rubber plantations, with effects varying by region and season. When assessing drought’s impact on rubber plantation GPP or carbon sequestration, it is essential to consider differences in drought thresholds within the climatic context.