The generation of membrane curvature in intracellular traffic involves many proteins that can curve lipid bilayers. Among these, dynamin-like proteins were shown to deform membranes into tubules, and thus far are the only proteins known to mechanically drive membrane fission. Because dynamin forms a helical coat circling a membrane tubule, its polymerization is thought to be responsible for this membrane deformation. Here we show that the force generated by dynamin polymerization, 18 pN, is sufficient to deform membranes yet can still be counteracted by high membrane tension. Importantly, we observe that at low dynamin concentration, polymer nucleation strongly depends on membrane curvature. This suggests that dynamin may be precisely recruited to membrane buds' necks because of their high curvature. To understand this curvature dependence, we developed a theory based on the competition between dynamin polymerization and membrane mechanical deformation. This curvature control of dynamin polymerization is predicted for a specific range of concentrations (∼0.1–10 μM), which corresponds to our measurements. More generally, we expect that any protein that binds or self-assembles onto membranes in a curvature-coupled way should behave in a qualitatively similar manner, but with its own specific range of concentration.