The mechanistic target of rapamycin complex 1 (mTORC1) kinase controls growth in response to nutrients, including the amino acid leucine. In cultured cells, mTORC1 senses leucine through the leucine-binding Sestrin proteins, but the physiological functions and distribution of Sestrin-mediated leucine sensing in mammals are unknown. We find that mice lacking Sestrin1 and Sestrin2 cannot inhibit mTORC1 upon dietary leucine deprivation and suffer a rapid loss of white adipose tissue (WAT) and muscle. The WAT loss is driven by aberrant mTORC1 activity and fibroblast growth factor 21 (FGF21) production in the liver. Sestrin expression in the liver lobule is zonated, accounting for zone-specific regulation of mTORC1 activity and FGF21 induction by leucine. These results establish the mammalian Sestrins as physiological leucine sensors and reveal a spatial organization to nutrient sensing by the mTORC1 pathway.