We exploit three distinct monetary policy tools, monetary tightening shocks, central bank announcements and a machine-learning measure of climate-specific forward guidance to assess how they shape corporate climate risk exposure. Monetary tightening increases firms’ climate risk exposure, with the effect being more pronounced among high-emission firms. The effect is stronger in Europe than in the United States. Beyond exposure, =monetary tightening shifts the composition of corporate innovation, reducing green patenting by more than non-green patenting. Positive information shocks reduce climate exposure for European firms. Targeted ECB climate-related forward guidance causally increases brown firms' climate risk exposure. The increase reflects an additional anticipation ("green paradox") channel, in which these firms front-load emissions-intensive production ahead of future climate-policy tightening that the guidance signals. These findings operate through a unified cost-of-capital channel where higher discount rates disproportionately penalize long-horizon decarbonization investments relative to short-duration carbon-intensive projects. Our work documents a novel and counterproductive role for both conventional monetary tools and central bank communication in the green transition.