Climate change poses escalating threats to health systems, particularly in low-resource settings like Nepal, where extreme weather events and chronic stressors challenge service delivery. Despite Nepal's high vulnerability, little is known about the enablers and barriers that underpin its health system's resilience to climate change. We conducted a qualitative study using semi-structured interviews with 26 key informants across Nepal's health system, including government officials, researchers, provincial workers and non-governmental organization (NGO) representatives. The World Health Organization Operational Framework for Building Climate-Resilient and Low-Carbon Health Systems guided thematic analysis to identify "enablers" - that is, facilitating factors - and barriers. Barriers significantly outweighed enablers. Enablers were sparse and largely not climate-specific. Notable climate-specific enablers included improved early warning systems and a Ministry of Health climate change focal point. Barriers included policymakers' limited climate literacy and prioritization; poor policy implementation; lack of managerial capacity and climate-health expertise; and inadequate infrastructure. Most enablers and barriers originated at governmental and health system levels. This study offers rare, empirically grounded insights into the factors that shape climate resilience of health systems in low-income settings such as Nepal, where climate change amplifies entrenched leadership, governance and capacity deficits. Strengthening everyday resilience, political will to tackle climate change and health challenges, and embedding climate considerations into health policy, workforce and infrastructure are critical. These are constructive insights not only for the federalizing Nepal health system but for global health systems confronting the dual challenges of climate change and systemic fragility, underscoring the urgent need for strong, clear leadership and governance.