The European Central Bank (ECB) has, albeit at a slow pace, started factoring in climate-related financial risks, on a par with other central banks. There is increasing pressure on the ECB to step into climate policy, notably due to the intensifying influence of climate activism on European politics and the adoption of the European Green Deal, which is advocated by all major political groups. This pressure is amplified by evidence that consecutive quantitative easing (QE) waves after 2015 have favoured carbon-intensive sectors over low-carbon, sustainable ones. Recent literature suggests, moreover, that environmentally unsustainable market incumbents, who saw their capital costs plummeting owing to QE, are sub-optimally overrepresented since they account for a relatively small share in terms of gross value added (GVA) to the Eurozone’s economy. The principle of ‘‘market neutrality’’, which strictly applies to the monetary policy operations of the ECB, is thus correlated with reproducing the current structure of the bond market, where carbon-intensive sectors make up a considerable share. This ‘‘carbon bias’’, which has distributional effects, undermines the secondary mandate of the ECB, according to which the bank has to support the general economic policies of the EU and, therefore, the cornerstone climate and energy policy of the bloc. Nevertheless, the ECB’s primary mandate of maintaining price stability is clearly prioritised in cases of trade-offs with the secondary mandate. According to an array of experts, steering monetary policy towards environmental sustainability can be achieved without impairing price stability. This paper briefly discusses some of the solutions that will enable the ECB to complement the climate policy of the EU and national governments. It is essential, though, to comprehend that the ECB cannot substitute public climate policy.