Corporate Social Responsibility (CSR) literature in developed countries indicates that there are two types of CSR (i.e., proactive CSR and reactive CSR), and only the proactive one can boost innovation. However, recent studies from emerging economies such as China show that both types of CSR can enhance innovation. Such inconsistent results may be created by, on the one hand, the heterogeneity of innovation types, and on the other hand, the heterogeneity of mechanisms though which CSR impacts innovation in different countries. Accordingly, this paper theoretically explores the impacts of two types of CSR (i.e., proactive CSR and reactive CSR) on two of innovation types (exploratory innovation and exploitative innovation). This paper further reveals the mechanisms through which CSR impacts innovation in China by investigating the moderating role of institutional support (i.e., government support and social support) on the relationship between CSR and innovation. Using a panel dataset (2008–2016) of 286 Chinese public listed firms from research and development (R&D)-intensive industries (e.g., information technology, pharmaceutical and biological products; and chemicals, etc.), our findings show that: (1) proactive CSR promotes exploratory innovation; (2) reactive CSR promotes exploitative innovation; (3) government support strengthen the relationship between proactive CSR and exploratory innovation as well as the relationship between reactive CSR and exploitative innovation; (4) social support weaken the relationship between proactive CSR and exploratory innovation. This paper enriches our understanding on the relationship between CSR and innovation, and provides implications for practitioners and policymakers.