Carbon information disclosure (CID) has become central to corporate climate governance. Drawing on annual customer–supplier data, this study examines how customer ESG performance influences suppliers’ carbon disclosure. The results show that customer ESG initiatives significantly enhance supplier CID, particularly in the social and governance dimensions. Mechanism analysis identifies two underlying mechanisms: a conceptual dimension (i.e., fostering the convergence of green values) and a practical dimension (i.e., intensifying supplier competition). Heterogeneity analysis further reveals that the impact of ESG is stronger when the customer is a state-owned enterprise, when the supplier operates in a heavily polluting industry, or when the supplier faces stricter external environmental regulations. Furthermore, through the lens of supply chain influence, we examine potential “pandering” in supplier CID behavior. The results indicate that suppliers’ CID more closely reflects actual practices when customers hold greater influence, but tends to be exaggerated when suppliers hold greater influence. This study offers a novel perspective for advancing supply chain carbon management.