Photovoltaic devices based on hybrid perovskite materials have exceeded 22% efficiency due to high charge-carrier mobilities and lifetimes. Properties such as photocurrent generation and open-circuit voltage are influenced by the microscopic structure and orientation of the perovskite crystals, but are difficult to quantify on the intra-grain length scale and are often treated as homogeneous within the active layer. Here, we map the local short-circuit photocurrent, open-circuit photovoltage, and dark drift current in state-of-the-art methylammonium lead iodide solar cells using photoconductive atomic force microscopy. We find, within individual grains, spatially correlated heterogeneity in short-circuit current and open-circuit voltage up to 0.6 V. These variations are related to different crystal facets and have a direct impact on the macroscopic power conversion efficiency. We attribute this heterogeneity to a facet-dependent density of trap states. These results imply that controlling crystal grain and facet orientation will enable a systematic optimization of polycrystalline and single-crystal devices for photovoltaic and lighting applications.