We quantify the role of bank credit in shaping the short-run effects of climate policy shocks on the economy. Using carbon policy surprises from the EU-ETS, we document that higher carbon prices, while successfully reducing emissions, lead to lower economic activity, lower bank equity and tightening of credit supply. We interpret these empirical facts through the lens of a dynamic stochastic general equilibrium model with polluting and non-polluting sectors, nominal price rigidities, and credit market frictions both in the financial and non-financial sectors. The model successfully matches the empirical impulse responses of key aggregates to carbon price shocks. Counterfactual simulations suggest that the bank lending channel plays a quantitatively meaningful role in propagating the climate policy shocks. Finally, implications for the optimal design of monetary and macroprudential policies are explored.