We study bank capital requirements as a tool to address climate-related financial risks and evaluate whether a prudential mandate for bank regulators remains appropriate in the presence of carbon externalities. We show that a prudential mandate maximizes welfare if carbon taxes are set optimally and fully characterize optimal capital requirements under such a mandate. Optimal transition-risk adjustments can crowd out clean lending. When carbon pricing is insufficient, using capital requirements to address externalities can require sacrificing financial stability or prove altogether ineffective. Capital requirements can play an indirect role by mitigating stranded asset risk, thereby making future carbon taxes credible.