A polarization transformation can be fully described by a 4 × 4 matrix, known as the Mueller matrix. To fully image an object's polarization response, one needs to compute the Mueller matrix at each pixel of the image. Standard divison-of-time Mueller matrix imaging, because of its sequential nature, is ill-suited to applications requiring immediate and real-time imaging and is also bulky owing to multiple moving parts. In this work, we propose a new method for compact, snapshot Mueller matrix imaging, based on structured polarization illumination, and division-of-focal plane imaging, which can, in a single-shot, fully capture the Mueller matrix information of a band-limited signal.