Artificial Intelligence (AI) in medical applications holds great promise. However, the use of Machine Learning-based (ML) systems in clinical practice is still minimal. It is uniquely difficult to introduce clinician-facing ML-based systems in practice, which has been recognised in HCI and related fields. Recent publications have begun to address the sociotechnical challenges of designing, developing, and successfully deploying clinician-facing ML-based systems. We conducted a qualitative systematic review and provided answers to the question: "How can HCI researchers and practitioners contribute to the successful realisation of ML in medical practice?"We reviewed 25 eligible papers that investigated the real-world clinical implications of concrete clinician-facing ML-based systems. The main contributions of this systematic review are: (1) an overview of the technical aspects of ML innovation and their consequences for HCI researchers and practitioners; (2) a description of the different roles that ML-based systems can take in clinical settings; (3) a conceptualisation of the main activities of medical ML innovation processes; (4) identification of five sociotechnical interdependencies that emerge from medical ML innovation; and (5) implications for HCI researchers and practitioners on how to mitigate the sociotechnical challenges of medical ML innovation.