Food waste (FW) represents one of the greatest concerns facing mankind today; thus, the UN Agenda 2030 for Sustainable Development establishes that it must be halved by 2030. European Union legislators have taken part in this debate by publishing Directive 2018/851 to monitor the FW reduction goals, according to the waste hierarchical pyramid approach. At present, there are several proposed FW hierarchical pyramids, but these do not regard the associations between the level of waste-tackling strategies and social innovation (SI) models. Thus, the paper aims to build a hierarchical pyramid that considers, for each step of the food-supply chain and each level of the pyramid, all the FW social innovation models. A qualitative analysis of academic studies, institutional documents, and specific projects has been conducted. The results confirm the gap in the scientific literature and the lack of a systematic classification of SI activities to reduce FW. Furthermore, current SI practices are actually more focused on the human reuse of FW than on prevention, whereas SI models based on prevention might return the FWL issue to its systematic dimension. This information will help policymakers to reconsider the structural causes of FW inside the agro-food system, and not only its final consequences.