The rapid deployment of artificial intelligence in healthcare analytics has outpaced the development of governance structures needed to monitor, audit, and ensure the continuing safety and equity of these systems. This gap is especially consequential when models influence clinical prioritization, operational resource allocation, or population health management. This systematic review critically examined literature on artificial intelligence governance for healthcare analytics. The review focused on model monitoring, bias auditing, data drift detection, accountability structures, and regulatory readiness. A PRISMA 2020–aligned search strategy was applied across PubMed, Scopus, IEEE Xplore, and Web of Science. Dual screening, structured data extraction, and narrative synthesis were used to evaluate frameworks, tools, implementation practices, and reported barriers. The review found numerous frameworks and methods addressing individual governance tasks, including performance monitoring, calibration surveillance, fairness assessment, and documentation. However, comprehensive governance systems that integrate technical monitoring with organizational accountability in live healthcare environments remained uncommon. Artificial intelligence governance in healthcare analytics remains fragmented and inconsistently operationalized. Monitoring and drift detection were comparatively more mature than accountability structures, bias audit workflows, and regulatory readiness practices.