Climate change is having unprecedented impacts on human health, including increasing infectious disease risk. Despite this, health systems across the world are currently not prepared for novel disease scenarios anticipated with climate change. While the need for health systems to develop climate change adaptation strategies has been stressed in the past, there is no clear consensus on how this can be achieved, especially in rural areas in low- and middle-income countries that experience high disease burdens and climate change impacts simultaneously. Here, we highlight the need to put health systems in the context of climate change and demonstrate how this can be achieved by taking into account all aspects of infectious disease risk (i.e., pathogen hazards, and exposure and vulnerability to these pathogen hazards). The framework focuses on rural communities in East Africa since communities in this region experience climate change impacts, present specific vulnerabilities and exposure to climate-related hazards, and have regular exposure to a high burden of infectious diseases. Implementing the outlined approach can help make health systems climate adapted and avoid slowing momentum towards achieving global health grand challenge targets.