Mueller matrices provide a complete description of a medium’s response to excitation by polarized light, and their characterization is important across a broad range of applications from ellipsometry in material science to polarimetry in biochemistry, medicine and astronomy. Here we introduce single-shot Mueller matrix polarimetry based on generalized measurements performed with a Poincaré beam. We determine the Mueller matrix of a homogeneous medium with unknown optical activity by detecting its optical response to a Poincaré beam, which across its profile contains all polarization states, and analyze the resulting polarization pattern in terms of four generalized measurements, which are implemented as a path-displaced Sagnac interferometer. We illustrate the working of our Mueller matrix polarimetry on the example of tilted and rotated wave plates and find excellent agreement with predictions as well as alternative Stokes measurements. After initial calibration, the alignment of the device stays stable for up to 8 hours, promising suitability for the dynamic characterization of Mueller matrices that change in time. Unlike traditional rotating waveplate polarimetry, our method allows the acquisition of a sample’s dynamic Mueller matrix. We expect that our feasibility study could be developed into a practical and versatile tool for the real-time analysis of optical activity changes, with applications in biomedical and biochemical research and industrial monitoring.