We present an approach for rapidly and quantitatively mapping tissue absorption and scattering spectra in a wide-field, noncontact imaging geometry by combining multifrequency spatial frequency domain imaging (SFDI) with a computed-tomography imaging spectrometer (CTIS). SFDI overcomes the need to spatially scan a source, and is based on the projection and analysis of periodic structured illumination patterns. CTIS provides a throughput advantage by simultaneously diffracting multiple spectral images onto a single CCD chip to gather spectra at every pixel of the image, thus providing spatial and spectral information in a single snapshot. The spatial-spectral data set was acquired 30 times faster than with our wavelength-scanning liquid crystal tunable filter camera, even though it is not yet optimized for speed. Here we demonstrate that the combined SFDI-CTIS is capable of rapid, multispectral imaging of tissue absorption and scattering in a noncontact, nonscanning platform. The combined system was validated for 36 wavelengths between 650-1000 nm in tissue simulating phantoms over a range of tissue-like absorption and scattering properties. The average percent error for the range of absorption coefficients (μa) was less than 10% from 650-800 nm, and less than 20% from 800-1000 nm. The average percent error in reduced scattering coefficients (μs') was less than 5% from 650-700 nm and less than 3% from 700-1000 nm. The SFDI-CTIS platform was applied to a mouse model of brain injury in order to demonstrate the utility of this approach in characterizing spatially and spectrally varying tissue optical properties.