The urgency of estimating the impact of climate risks on the financial system is increasingly recognized among scholars and practitioners. By adopting a network approach to financial dependencies, we look at how climate policy risk might propagate through the financial system. We develop a network-based climate stress-test methodology and apply it to large Euro Area banks in a ‘green’ and a ‘brown’ scenario. We find that direct and indirect exposures to climate-policy-relevant sectors represent a large portion of investors’ equity portfolios, especially for investment and pension funds. Additionally, the portion of banks’ loan portfolios exposed to these sectors is comparable to banks’ capital. Our results suggest that climate policy timing matters. An early and stable policy framework would allow for smooth asset value adjustments and lead to potential net winners and losers. In contrast, a late and abrupt policy framework could have adverse systemic consequences.