Vietnam is among the most vulnerable countries in the world regarding climate change. Climate-related hazards already affect human health and the health system in Vietnam. As the health system plays an important role in individual and community-level resilience, their components—such as healthcare facilities, health services, health workforces, and health supply chains—must continue to adapt to current and future challenges including climate change. This paper investigates the impacts of climate change on the Vietnamese health system and suggests strategies for health system practitioners to apply a climate lens and build a comprehensive approach to promoting resilient primary healthcare and health security. Analysis involved systematic literature and policy reviews, supplemented by two focus group discussions. The results showed that climatic factors such as temperature and rainfall show complex patterns of change across Vietnam. Natural disasters and extreme weather events occur every year across the country, causing human and physical damage in general and to the health sector in particular. Given the context, efforts have been made to develop and promote measures that can help the health sector in Vietnam overcome climate change challenges, evidenced in several national regulations and policies of Vietnam. Despite increased efforts to focus on climate and health, development challenges persist. Policy-related recommendations are proposed to further enhance the health sector to more effectively respond to climate change. They include establishing an early warning system, developing a climate-health database, vulnerability and adaptation mapping, and the scaling up of successful models on water, sanitation, and hygiene. Vietnam’s case is likely, in many aspects, to be also relevant to other developing countries.