Clinical decision-making and radiology will inevitably be transformed by artificial intelligence (AI) in the coming years. The rapid adoption of AI in this domain, and in other everyday applications, has brought an increased awareness of the potential impacts and negative consequences that may occur throughout the sociotechnical systems that these technologies are implemented in. In this paper, we review and apply a previously published taxonomy of the sociotechnical harms of AI to investigate how these harms could manifest during the development and clinical implementation of AI-based medical image analysis. Through an illustrative case study example on computer-aided diagnosis using brain magnetic resonance imaging, we demonstrate how performing impact assessments of sociotechnical harms can assist in operationalizing the medical ethics principle of non-maleficence, thereby guiding the ethical development and implementation of AI technologies in healthcare.