Improved health data governance is urgently needed due to the increasing use of digital technologies that facilitate the collection of health data and growing demand to use that data in artificial intelligence (AI) models that contribute to improving health outcomes. While most of the discussion around health data governance is focused on policy and regulation, we present a practical perspective. We focus on the context of low-resource government health systems, using first-hand experience of the Zanzibar health system as a specific case study, and examine three aspects of data governance: informed consent, data access and security, and data quality. We discuss the barriers to obtaining meaningful informed consent, highlighting the need for more research to determine how to effectively communicate about data and AI and to design effective consent processes. We then report on the process of introducing data access management and information security guidelines into the Zanzibar health system, demonstrating the gaps in capacity and resources that must be addressed during the implementation of a health data governance policy in a low-resource government system. Finally, we discuss the quality of service delivery data in low-resource health systems such as Zanzibar’s, highlighting that a large quantity of data does not necessarily ensure its suitability for AI development. Poor data quality can be addressed to some extent through improved data governance, but the problem is inextricably linked to the weakness of a health system, and therefore AI-quality data cannot be obtained through technological or data governance measures alone.