Responsible Innovation in Health (RIH) represents an emerging Science, Technology and Innovation (STI) approach that could support not only the Sustainable Development Goal (SDG) “Good health and well-being” but also other SDGs. Since few studies have conceptualized the relationships between RIH and the SDGs, our goal was to inductively develop a framework to identify knowledge gaps and areas for further reflections. Our exploratory study involved: (1) performing a web-based horizon scanning to identify health innovations with responsibility features; and (2) illustrating through empirical examples how RIH addresses the SDGs. A total of 105 innovations were identified: up to 43% were developed by non-profit organizations, universities or volunteers; 46.7% originated from the United States; and 64.5% targeted countries in Africa, Central and South America and South Asia. These innovations addressed health problems such as newborn care (15.5%), reduced mobility and limb amputation (14.5%), infectious diseases (10.9%), pregnancy and delivery care (9.1%) and proper access to care and drugs (7.3%). Several of these innovations were aligned with SDG10-Reduced inequalities (87%), SDG17-Partnerships for the goals (54%), SDG1-No poverty (15%) and SDG4-Quality education (11%). A smaller number of them addressed sustainable economic development goals such as SDG11-Sustainable cities and communities (9%) and SDG9-Industry and innovation (6%), and environmental sustainability goals such as SDG7-Affordable and clean energy (7%) and SDG6-Clean water and sanitation (5%). Three examples show how RIH combines entrepreneurship and innovation in novel ways to address the determinants of health, thereby contributing to SDG5 (Gender), SDG10 (Inequalities), SDG4 (Education) and SDG8 (Decent work), and indirectly supporting SDG7 (Clean energy) and SDG13 (Climate action). Further research should examine how alternative business models, social enterprises and social finance may support the STI approach behind RIH.