A supply chain’s risk spillover effect will affect the customer’s risk on the financing constraints of suppliers. This paper builds on the evaluation of customer risk by fuzzy mathematics, combines with the A-share listed companies in Shanghai and Shenzhen from 2007 to 2019 as a study sample, and empirically inspects the influence of customer risk on the level of corporate financing constraints. According to the study, it shows that the customer risk is currently at a moderate level, which will notably impair the supplier’s external financing ability. This phenomenon is more remarkable when the monetary policy is tightened with fierce competition in the industry. This paper unveils the economic consequences of customer risk spillovers from a supply chain, enriches the study of the generation mechanism of corporate financing constraints, and provides investors and regulators with empirical evidence to appreciate corporate financing constraints.