Mycobacterium tuberculosis (MTB) remains a major challenge to global health made worse by the spread of multidrug resistance. We therefore examined whether stimulating intracellular killing of mycobacteria through pharmacological enhancement of macroautophagy might provide a novel therapeutic strategy. Despite the resistance of MTB to killing by basal autophagy, cell-based screening of FDA-approved drugs revealed two anticonvulsants, carbamazepine and valproic acid, that were able to stimulate autophagic killing of intracellular M. tuberculosis within primary human macrophages at concentrations achievable in humans. Using a zebrafish model, we show that carbamazepine can stimulate autophagy in vivo and enhance clearance of M. marinum, while in mice infected with a highly virulent multidrug-resistant MTB strain, carbamazepine treatment reduced bacterial burden, improved lung pathology and stimulated adaptive immunity. We show that carbamazepine induces antimicrobial autophagy through a novel, evolutionarily conserved, mTOR-independent pathway controlled by cellular depletion of myo-inositol. While strain-specific differences in susceptibility to in vivo carbamazepine treatment may exist, autophagy enhancement by repurposed drugs provides an easily implementable potential therapy for the treatment of multidrug-resistant mycobacterial infection.