We have accurately determined the exciton binding energy and reduced mass of single crystals of methylammonium lead triiodide using magneto-reflectivity at very high magnetic fields. The single crystal has excellent optical properties with a narrow line width of ∼3 meV for the excitonic transitions and a 2s transition that is clearly visible even at zero magnetic field. The exciton binding energy of 16 ± 2 meV in the low-temperature orthorhombic phase is almost identical to the value found in polycrystalline samples, crucially ruling out any possibility that the exciton binding energy depends on the grain size. In the room-temperature tetragonal phase, an upper limit for the exciton binding energy of 12 ± 4 meV is estimated from the evolution of 1s-2s splitting at high magnetic field.