Although existing research emphasizes the importance of internal carbon management (CM) in influencing firm risk, the impact of external stakeholder CM on firm risk remains unclear. This study employs signaling theory to explore how supplier CM affects firm idiosyncratic risk (IR), alongside the moderating roles of the supply chain information environment and the criticality of firm–supplier relationships. The findings of this study demonstrate that supplier CM can reduce firm IR. The risk reduction effect is strong when the information environment between a firm and its suppliers is rich and when the dependency between the firm and its supplier is strong. Path analysis reveals that supplier CM primarily reduces firm IR by alleviating information asymmetry. Moreover, the risk reduction effect increases for firms with small sizes. This research extends the application of signaling theory to supply chain research and bridges the gap between the CM and firm IR literature within the context of supply chain management.