During mitochondrial fission, key molecular and cellular factors assemble on the outer mitochondrial membrane, where they coordinate to generate constriction. Constriction sites can eventually divide or reverse upon disassembly of the machinery. However, a role for membrane tension in mitochondrial fission, although speculated, has remained undefined. We capture the dynamics of constricting mitochondria in mammalian cells using live-cell structured illumination microscopy (SIM). By analyzing the diameters of tubules that emerge from mitochondria and implementing a fluorescence lifetime-based mitochondrial membrane tension sensor, we discover that mitochondria are indeed under tension. Under perturbations that reduce mitochondrial tension, constrictions initiate at the same rate, but are less likely to divide. We propose a model based on our estimates of mitochondrial membrane tension and bending energy in living cells which accounts for the observed probability distribution for mitochondrial constrictions to divide.