Abstract The Amazon rainforest is highly biodiverse and the largest intact, tropical forest in the world. Undisturbed tropical forests act as a carbon sink by taking up about 15% of anthropogenic carbon emissions per year. In the past decades, a declining trend in the carbon sink capacity in the Amazon rainforest has been observed due to increased carbon losses and tree mortality. The causes are disputed, but increasing temperatures and more frequent severe droughts are potentially major drivers. We employ a novel modelling framework and hypothesize that previously rare, extreme droughts in the Amazon, such as the ones in 2005 and 2010, constitute the main cause behind the decline of the net carbon sink in aboveground biomass. Our dynamic vegetation model simulates process-based plant hydraulics and drought-induced mortality, and accounts for the diversity of strategies in plant responses to drought based on observed hydraulic vulnerability curves. The simulated impact of the 2005 drought event temporarily turned the annual Amazon net carbon sink to a carbon source of about 0.25 MgC ha-1. In contrast to other dynamic vegetation models our model simulated an increasing trend in carbon losses and a declining trend in the Amazon carbon sink over the past 25 years (net sink rate of -0.018 Mg C ha-1 year-1 or -0.22 Mg C ha-1 per decade) which corresponds well with long-term forest monitoring data (net sink rate of -0.016 Mg C ha-1 year-1). We show that this trend is entirely attributable to drought-induced forest mortality during extreme years. The simulations show a threshold-like behaviour between drought intensity and biomass loss, which is due to xylem vulnerability, indicating the potentially high sensitivity of Amazon forests to extreme drought. Further increases in the severity and frequency of droughts might thus lead to greater carbon release and tree mortality than previously assumed.