The Shockley-Queisser limit for solar cell efficiency can be overcome if hot carriers can be harvested before they thermalize. Recently, carrier cooling time up to 100 picoseconds was observed in hybrid perovskites, but it is unclear whether these long-lived hot carriers can migrate long distance for efficient collection. We report direct visualization of hot-carrier migration in methylammonium lead iodide (CH₃NH₃PbI₃) thin films by ultrafast transient absorption microscopy, demonstrating three distinct transport regimes. Quasiballistic transport was observed to correlate with excess kinetic energy, resulting in up to 230 nanometers transport distance that could overcome grain boundaries. The nonequilibrium transport persisted over tens of picoseconds and ~600 nanometers before reaching the diffusive transport limit. These results suggest potential applications of hot-carrier devices based on hybrid perovskites.