We explore the ferroic properties of methylammonium lead iodide perovskite solar cells by piezoresponse force microscopy (PFM). In vertical and horizontal PFM imaging, we find domains of alternating polarization with a width of 90 nm which we identify as polarized ferroelectric domains. High-resolution photo-conductive atomic force micrographs under illumination also show alternating charge carrier extraction patterns which we attribute to the local vertical polarization components within the ferroelectric domains. The correlation of the sample properties with atomic force and kelvin probe force micrographs evidence the ferroelectric nature of the domains.