Green innovation is a key driving force in promoting the development of a low-carbon economy and society. However, previous studies have not paid enough attention to the influence of internal informal institutions on green innovation. To address this issue, this study conducts empirical tests by using a sample of A-share listed firms in China from 2013 to 2020. This study investigates whether and how carbon management strategies, as an important part of the internal informal institutions, promote corporate green innovation. The results show that carbon management strategies have a significant and positive impact on both the quantity and quality of green innovation. In addition, emphasizing meeting the needs of stakeholders and focusing on research and development (R&D) investment can significantly enhance the positive impact of carbon management strategies on green innovation. Furthermore, at the market level, carbon management strategies significantly boost green innovation in firms with larger market shares, which is enhanced by meeting stakeholder demands. At the firm level, state-owned enterprises pay attention to the mechanisms of both stakeholders’ demands and R&D investment in driving green innovation. At the executive level, executive shareholding firms emphasize driving green innovation through R&D investment. Overall, these findings provide new evidence for the determinants of green innovation that have not been fully explored before through the perspective of internal informal institutions.