A full Mueller polarimeter was implemented on a commercial laser-scanning microscope. The new polarimetric microscope is based on high-speed polarization modulation by spectral coding using a wavelength-swept laser as a source. Calibration as well as estimation of the measurement errors of the device are reported. The acquisition of Mueller images at the speed of a scanning microscope is demonstrated for the first time. Mueller images of mineral and biological samples illustrate this new polarimetric microscopy.