In the face of global climate change and the collision of consumer preferences towards green and low-carbon, businesses need to accelerate the transition to sustainable development to achieve long-term growth. Companies must raise significant funds to support this transition and manage high market risk. The existing research on green innovation within supply chains often overlooks market risks, particularly those associated with incomplete information. Hence, this paper considers a two-echelon supply chain system composed of a manufacturer and a retailer. Manufacturers are willing to carry out green innovation and make a single product for sale in the consumer market with green preferences. However, innovation is risky due to the uncertainty in the sales volume of green products. In addition, the manufacturer may lack internal capital to invest in the innovation activities and may seek external financial resources, e.g., bank loans or retail prepayment financing. Hence, the manufacturer and retailer must decide which financial option to adopt. The results show that when the market risk is high, the supply chain members tend to make conservative decisions, no matter which financial modes they choose. However, with the robust optimization approach, the manufacturer and the retailer may earn a higher profit when the market risk is high. When the prepayment rate and bank loan interest rate are equal, regardless of the market risk, the manufacturer’s optimal decision is to choose prepayment financing from the retailer. However, when the prepayment rate is higher than the bank loan interest rate, there is no dominant strategy for the manufacturer to choose.