Acute myeloid leukemia (AML) is maintained by self-renewing leukemic stem cells (LSCs). A fundamental problem in treating AML is that conventional therapy fails to eliminate LSCs, which can reinitiate leukemia. Heat shock transcription factor 1 (HSF1), a central regulator of the stress response, has emerged as an important target in cancer therapy. Using genetic Hsf1 deletion and a direct HSF1 small molecule inhibitor, we show that HSF1 is specifically required for the maintenance of AML, while sparing steady-state and stressed hematopoiesis. Mechanistically, deletion of Hsf1 dysregulates multifaceted genes involved in LSC stemness and suppresses mitochondrial oxidative phosphorylation through downregulation of succinate dehydrogenase C (SDHC), a direct HSF1 target. Forced expression of SDHC largely restores the Hsf1 ablation-induced AML developmental defect. Importantly, the growth and engraftment of human AML cells are suppressed by HSF1 inhibition. Our data provide a rationale for developing efficacious small molecules to specifically target HSF1 in AML.