The rapid evolution of artificial intelligence (AI) is structuralizing social, political, and economic determinants of health into the invisible algorithms that shape all facets of modern life. Nevertheless, AI holds immense potential as a public health tool, enabling beneficial objectives such as precision public health and medicine. Developing an AI governance framework that can maximize the benefits and minimize the risks of AI is a significant challenge. The benefits of public health engagement in AI governance could be extensive. Here, we describe how several public health concepts can enhance AI governance. Specifically, we explain how (1) harm reduction can provide a framework for navigating the governance debate between traditional regulation and "soft law" approaches; (2) a public health understanding of social determinants of health is crucial to optimally weigh the potential risks and benefits of AI; (3) public health ethics provides a toolset for guiding governance decisions where individual interests intersect with collective interests; and (4) a One Health approach can improve AI governance effectiveness while advancing public health outcomes. Public health theories, perspectives, and innovations could substantially enrich and improve AI governance, creating a more equitable and socially beneficial path for AI development.