Health Impacts of Nuclear War Act of 2023 This bill requires the Department of Health and Human Services (HHS) to evaluate the consequences of the environmental impacts of nuclear war on human health and the ability of the United States to address these consequences. Specifically, HHS must conduct a five-year research and preparedness program that addresses the environmental effects of explosions of nuclear weapons (e.g., vast quantities of soot) and the resulting impact on human health (e.g., increased cancer rates). HHS may implement the program directly, as well as through grants, contracts, and cooperative agreements with nonprofits, nonprofit research institutions, or institutions of higher education. Additionally, HHS must, in coordination with other specified agencies and stakeholders, assess the ability of U.S. health systems to respond to these health consequences and identify any critical gaps or uncertainties.