Family firms' governance, which is inherently risk-averse, frequently inhibits sustainable innovation. However, the same governance structure, driven by a strong desire for oversight, can enhance innovation outcomes by ensuring diligent monitoring and execution. This paper aims to conceptualise how governance bodies within family firms contribute to fostering sustainable innovation. To this end, we conducted a critical review to identify the state of the art of sustainable innovation and governance structure of family firms. Then, drawing on the dynamic capability theory, we developed a new theory combining literature with insights from an illustrative case study. The findings unveil that some family firm governance bodies champion sustainable innovation, yet their efforts are frequently confined to the same. Given the absence of a dedicated board to manage the innovation process end-to-end, we propose an emerging solution in managerial practice, known as a shadow board, to fill this gap. That is, a selected group of younger employees or external experts tasked with advising the executive team. The results shall guide scholars towards a better understanding of the underlying mechanisms that can drive sustainable innovation in family firms from a governance perspective. Moreover, by leveraging these insights, organisations can enhance their ability to overcome potential challenges and optimise sustainable innovation processes.