The Imaging X-ray Polarimetry Explorer, a NASA small explorer mission, will be the first mission dedicated to x-ray polarimetry. The payload consists of three identical telescopes, each comprising a mirror module assembly (MMA) with a polarization-sensitive detector at its focus. We describe all aspects of the MMA, from initial optical and mechanical design considerations to meet program requirements through mirror shell fabrication, mirror shell integration and module assembly, environmental testing, x-ray calibration, and on-ground and on-orbit alignment.