Excitation localization involving dynamic nanoscale distortions is a central aspect of photocatalysis, quantum materials and molecular optoelectronics. Experimental characterization of such distortions requires techniques sensitive to the formation of point-defect-like local structural rearrangements in real time. Here, we visualize excitation-induced strain fields in a prototypical member of the lead halide perovskites via femtosecond resolution diffuse x-ray scattering measurements. This enables momentum-resolved phonon spectroscopy of the locally-distorted structure and reveals radially-expanding nanometer-scale elastic strain fields associated with the formation and relaxation of polarons in photoexcited perovskites. Quantitative estimates of the magnitude and the shape of this polaronic distortion are obtained, providing direct insights into the debated dynamic structural distortions in these materials. Optical pump-probe reflection spectroscopy corroborates these results and shows how these large polaronic distortions transiently modify the carrier effective mass, providing a unified picture of the coupled structural and electronic dynamics that underlie the unique optoelectronic functionality of the hybrid perovskites.