Superconductors are excellent testbeds for studying vortices, topological excitations that also appear in superfluids, liquid crystals and Bose–Einstein condensates. Vortex motion can be disruptive; it can cause phase transitions, glitches in pulsars, and losses in superconducting microwave circuits, and it limits the current-carrying capacity of superconductors. Understanding vortex dynamics is fundamentally and technologically important, and the competition between thermal energy and energy barriers defined by material disorder is not completely understood. Specifically, early measurements of thermally activated vortex motion (creep) in iron-based superconductors unveiled fast rates (S) comparable to measurements of YBa₂Cu₃O_7−δ (refs ,,,,,). This was puzzling because S is thought to somehow correlate with the Ginzburg number (Gi), and Gi is significantly lower in most iron-based superconductors than in YBa₂Cu₃O_7−δ. Here, we report very slow creep in BaFe₂(As_0.67P_0.33)₂ films, and propose the existence of a universal minimum realizable S ∼ Gi^1/2(T/T_c) (T_c is the superconducting transition temperature) that has been achieved in our films and few other materials, and is violated by none. This limitation provides new clues about designing materials with slow creep and the interplay between material parameters and vortex dynamics.