The Amazon tropical forest is a vital component of the global carbon cycle and climate systems due to its large biomass, photosynthetic productivity and profound influence on atmospheric dynamics and circulation patterns1–4. Reducing uncertainty in its response to future climate change is crucial for refining future climate projections. Although many emergent constraints (ECs) have been proposed for uncertainties in climate change projections from Earth system models (ESMs), limited research has focused on the ECs for the carbon cycle5–7. Here, we propose a novel EC to constrain the uncertainty in the future response of the Amazon tropical forest carbon cycle to climate change across the ESM ensemble that contributed to the Coupled Model Intercomparison Project phase 6. We show that ESMs with larger recent past global mean temperature trends project hotter and drier future conditions in the Amazon tropical forest, resulting in a greater climate-driven loss of carbon uptake. The proposed EC lowers the upper bound of the carbon uptake loss from 0.6 GtC year-1 to 0.4 GtC year-1 and reduces the variance of the future climate-driven carbon loss projections by 34%. The proposed EC for the first time relates carbon and water cycles, clarifying the mechanism of the potential drying of the Amazon under future warming.