We are in the midst of a crisis of climate change and environmental degradation that will only get worse, unless significant changes are rapidly made. Globally, the healthcare sector causes a large share of our total environmental footprint: 4.4% of greenhouse gases. Sustainable healthcare has emerged as a way for healthcare sectors in high-income countries to help mitigate climate change by reducing their emissions. Whether global health should be sustainable and what ethical grounds might exist to support such a claim are not questions that have been investigated. The paper argues that global health practice-the delivery of health services to underserved populations in resource-poor areas of the world-should be sustainable as a matter of climate justice and solidarity. Reducing climate change-related risks and harms for the vulnerable is integral to the mission of global health and thus it is necessary to consider the climate impact of its practice. The field has a duty to provide sustainable health services that are responsive to climate change-related changes in the local burden of disease and to build sustainable health system infrastructure. Specific responsibilities for global health funders, managers, and implementers to uphold the duty are proposed. To conclude, the paper considers what limits might be placed on the duty to deliver sustainable global healthcare.