Objective: Stimulating the vitality of green and low-carbon science and technology innovations and realizing the goal of "dual-carbon" are inherent requirements for implementing a new development concept, building a new development pattern, and promoting high-quality development. Currently, the development of green innovation and transformation is at a critical stage, and the dynamics of green innovation and transformation is still an important research object worth exploring. China is participating in a vertical division of the labor system with greater depth, breadth, and efficiency through global value chains. However, most existing studies have simply attributed low-carbon innovation outcomes to a single policy or an element. Under the guidance of dual circulation and dual carbon goals, exploring key links between the value chain consumer demand and green innovation in economic activities is significant. When studying the dynamics of corporate green innovation, attention should be paid to the huge demand-side impacts and transmission of the value chain. Methods: Based on the division of labor and connection of product value chains, this study matches and integrates the green innovation database of the A-share listed companies from 2002 to 2020. Then, this paper constructs a time series of multiregional input-output tables based on the interprovincial multi-regional input-output tables compiled by the Development Research Center of The State Council in 2002, 2007, 2012 and 2017. To more clearly describe how demand-side shocks affect the behavioral decisions of enterprises under green and low-carbon transformation through input-output networks, this paper starts with analyzing the consumption-side demand of the value chain. Using a multiregional input-output model, this paper quantifies the direct and indirect impacts on the consumption-side demand caused by the interprovincial division of labor in each province and estimates the demand impact of the interprovincial trade in China. Further, it decomposes the consumption-side demand of the value chain into the local consumption-side demand and foreign consumption-side demand of the value chain. Results: The research findings are as follows: Consumer demand, transmitted through the value chain, contributes to improving local firms' green innovation levels, particularly in terms of original green invention patents. The value chain amplifies the impact of the market demand from other regions on the local market. Local firms participating in the dual circulation strategy and constructing a unified domestic market will benefit from the broader dynamics of the external market. State-owned enterprises bear greater social responsibility in low-carbon emissions, and the consumer demand in the value chain guides subsidies to enter the domain of invention patents more effectively. This effect exhibits specific spatial and temporal heterogeneity, stimulating high-tech sectors and enterprises to invest in green innovation, while large-scale enterprises and startups face limitations in green innovation. Conclusions: This paper connects the value chain and innovation chain under the connotation of the global value chain division of labor linkage. By quantifying the direct and indirect impacts on the consumption-side demand, the paper examines the impact of demand-side shocks on the level of green innovation on the supply side by adopting the multiregional input-output model to measure the effect of demand-side shocks on China's interprovincial trade. The research results provide policy implications for creating a unified domestic market under sustainable development, effectively integrating value and innovation chains, and fostering green innovation in enterprises.