The debate on whether central banks should consider climate change risks in their mandate could reach some informed consensus given it is explicit how monetary policy, directly and indirectly, interacts with environmental sustainability. To unriddle this issue, we touch upon a novel perspective by exploring how monetary policy moderates the influence of economic complexity and technological innovation on energy productivity and carbon productivity in the presence of the labour force participation ratio, trade openness, financial inclusion, and GDP. Our study builds upon the Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) structure, considering the Group of Seven (G7) countries as the analytical laboratory over the 1995–2019 period. The principal outcomes based on the novel Method of Moments Quantile Regression (MMQR) are as follows: A higher level of economic complexity is associated with enhanced environmental sustainability. In addition, technological innovation is beneficial to environmental sustainability, especially across countries reporting moderate levels of environmental sustainability. Considering the direct impact, contractionary monetary policy deteriorates environmental sustainability, while expansionary monetary policy promotes it for green central banking in place. Regarding the moderating impacts, expansionary monetary policy is unveiled to manifest beneficial environmental impacts of economic complexity and technological innovation, provided that inflationary pressures remain under control. Based on our findings, it is recommended to formulate a monetary policy inclusive of climate‐related risks to capitalize on the environmentally favourable impacts of economic complexity and technological innovation. Finally, the monetary expansions keeping the inflationary pressures under control would benefit environmental sustainability.