Applying time-resolved electroabsorption spectroscopy for the first time to methylammonium lead triiodide perovskite (MAPbI3) thin films under reverse bias, we monitored optically the ultrafast evolution of the local counter-electric field produced by the drift of photogenerated electrons and holes in opposite directions. Under an externally applied electric field of |E| < 10^5 V cm–1, the carriers were found to reach a separation of 40 nm within ∼1 ps. This distance corresponds to the average dimensions of crystalline grains in the active film, at the boundaries of which charges were trapped. An intragrain average carrier drift mobility of μ± = 23 cm^2 V–1 s–1 was inferred. Subsequent charge detrapping, migration through the entire film, and accumulation at its insulated surfaces caused a blue shift of the perovskite absorption edge that arose within tens of picoseconds, owing to a trap-limited electron drift mobility μn = 6 cm^2 V–1 s–1. Charge recombination was entirely suppressed between field-separated photocarriers generated at initial densities of n0 ≤ 2 × 10^16 cm–3. Accumulation of electrons at the interface between a mesoporous TiO2 electron-transport layer and a multigrain MAPbI3 film was also observed, which was indicative of delayed charge injection through a poor contact junction.