There is much interest in cultured (cultivated) meat as a potential solution to concerns over the ecological and environmental footprint of food production, especially from animal‐derived food products. The aim of this critical review is to undertake a structured analysis of existing literature to (i) identify the range of materials that could be used within the cultured meat process; (ii) explore the potential biological and chemical food safety issues that arise; (iii) identify the known and also novel aspects of the food safety hazard portfolio that will inform hazard analysis and risk assessment approaches, and (iv) position a responsible innovation framework that can be utilized to mitigate food safety concerns with specific emphasis on cultured meat. Although a number of potential food safety hazards are identified that need to be considered within a food safety plan, further research is required to validate and verify that these food safety hazards have been suitably controlled and, where possible, eliminated. The responsible innovation framework developed herein, which extends beyond hazard analysis and traditional risk assessment approaches, can be applied in multiple contexts, including this use case of cultured meat production.