Climate change was recognized as a risk for ecosystems and the economy, and recently for the stability of the financial system. Tackling climate change requires urgent investments in the low-carbon energy transition. However, capital is not flowing at the pace and amount needed, exposing public and private investments to the risk of stranded assets. Central banks’ influence in the economy soared since 2008 but their role in the low-carbon transition has been mostly neglected so far. In this article, we display under which conditions central banks could contribute to meet the interlinked goals of sustainability and financial stability by influencing the timing and magnitude of the low-carbon transition. By further developing the EIRIN Stock-Flows Consistent, flow-of-funds behaviorual model, we simulate three scenarios, i.e. an unconditioned Quantitative Easing (QE), a green QE conditional to the purchase of green sovereign bonds, and conventional monetary policies. For each scenario, we analyze the impact on green investments and jobs, credit conditions, green/brown bonds market, and inequality across heterogeneous households and sectors, identifying main feedback loops and transmission channels. We find that, under the model’s conditions, a green QE promotes a faster development of the green bonds’ market, with positive spillovers on green investments, employment, commercial and central banks’ reserves, and on decreasing risk of stranded assets for the financial system. However, in all scenarios we find that wealth concentration in the credit sector and in the wealthiest household increases, with undesirable effects on income inequality, financial stability and aggregate demand.