In recent years, it has become almost axiomatic that biomedical research and clinical practice should be ‘innovative’—that is, that they should be always evolving and directed towards the production, translation and implementation of new technologies and practices. While this drive towards innovation in biomedicine might be beneficial, it also raises serious moral, legal, economic and sociopolitical questions that require further scrutiny. In this article, we argue that biomedical innovation needs to be accompanied by a dedicated ‘bioethics of innovation’ that attends systematically to the goals, process and outcomes of biomedical innovation as objects of critical inquiry. Using the example of personalised or precision medicine, we then suggest a preliminary framework for a bioethics of innovation, based on the research policy initiative of ‘Responsible Innovation’. We invite and encourage critiques of this framework and hope that this will provoke a challenging and enriching new bioethical discourse.