The European Union (EU) views the carbon border adjustment mechanism (CBAM) as a measure to tackle carbon leakage, which will have a profound impact on non-EU countries’ exports. Policymakers are faced with the question of how to deal with the CBAM. In contrast to previous studies, we explore the effects of the CBAM on non-EU countries from a dynamic game perspective. This study analyzed the potential effects of the CBAM on China and found that the government and export companies are the two main stakeholders. We found that they can both choose whether to respond actively or passively. Based on their interactive relationship, we adopted an evolutionary game to model the nexus between the government and export companies. We analyzed the evolutionary stable state of each stakeholder and the whole game with the replicator dynamic equation system. To make the system evolve to the optimal state where the government reacts actively and export companies implement low-carbon production, we provide a policy mechanism for how to set key parameters’ values. We used numerical simulation to verify the policy design and to conduct sensitivity analyses of the key parameters. Our results show that, when two stakeholders positively react to the CBAM, it is necessary to increase their profits and to reduce their costs. Therefore, some suggestions are proposed, including optimizing the trade structure, strengthening cooperation with the EU, improving the current carbon market, and adopting carbon tax.