Magnetic resonance imaging (MRI) is a widely used biomedical imaging modality that derives much of its contrast from microscale magnetic field patterns in tissues. However, the connection between these patterns and the appearance of macroscale MR images has not been the subject of direct experimental study due to a lack of methods to map microscopic fields in biological samples. Here, we optically probe magnetic fields in mammalian cells and tissues with submicron resolution and nanotesla sensitivity using nitrogen-vacancy diamond magnetometry, and combine these measurements with simulations of nuclear spin precession to predict the corresponding MRI contrast. We demonstrate the utility of this technology in an in vitro model of macrophage iron uptake and histological samples from a mouse model of hepatic iron overload. In addition, we follow magnetic particle endocytosis in live cells. This approach bridges a fundamental gap between an MRI voxel and its microscopic constituents.