We examine how firm-level climate risk affects cross-border merger and acquisition (M&A) initiation using 54,389 firm-year observations for Chinese A-share listed firms from 2000 to 2023. The results show that higher climate risk is associated with a significantly lower probability of initiating cross-border M&A. This finding remains robust across alternative measures, clustering levels, model specifications, placebo tests, lagged-variable analyses, an instrumental-variable strategy, and an event study based on an exogenous climate shock. Mechanism analyses provide evidence consistent with two channels: climate risk lowers firm value and reallocates financial and managerial resources toward green investment, thereby reducing the resources available for foreign acquisitions. The negative relationship is primarily driven by chronic physical risk and transition risk, whereas acute physical risk becomes significant only among climate-sensitive firms. The relationship is stronger among firms outside high-carbon industries and substantially weaker for green cross-border M&A, indicating that green acquisitions are relatively more resilient to climate-related pressures. Transaction-margin analyses further show that climate risk reduces the unconditional number of cross-border transactions but does not significantly affect completion probability or deal value conditional on initiation. Stronger ESG performance and greater executive overseas experience mitigate the negative relationship. Finally, among firms that undertake cross-border M&A, a larger climate risk attention gap is associated with lower cumulative abnormal returns, less favorable changes in operating performance, and higher financial leverage. These findings show that climate risk constrains firms’ foreign expansion decisions while firm capabilities, transaction characteristics, and climate-risk attention shape the extent and consequences of this constraint.