A novel spectroscopic Mueller-matrix polarimeter based on channeled spectropolarimetry is presented. It incorporates two high-order retarders and two Savart plates so that a spectrum modulated in both spatial and spectral axes are obtained from a two-dimensional CCD attached to a spectrometer. Two-dimensional Fourier analysis of the spectrum allows us to demodulate wavenumber-resolved Mueller matrix of the sample. The polarimeter uses no mechanical or active elements for polarization modulation and the snapshot measurement of sixteen Mueller-matrix elements can be achieved. Its feasibility was experimentally demonstrated in the spectral range between 500 and 750 nm.