Extending the wavelength range of spatial frequency domain imaging (SFDI) into the short-wave infrared (SWIR) has the potential to provide enhanced sensitivity to chromophores such as water and lipids that have prominent absorption features in the SWIR region. Here, we present, for the first time, a method combining SFDI with unstructured (zero spatial frequency) illumination to extract tissue absorption and scattering properties over a wavelength range (850 to 1800 nm) largely unexplored by previous tissue optics techniques. To obtain images over this wavelength range, we employ a SWIR camera in conjunction with an SFDI system. We use SFDI to obtain in vivo tissue reduced scattering coefficients at the wavelengths from 850 to 1050 nm, and then use unstructured wide-field illumination and an extrapolated power-law fit to this scattering spectrum to extract the absorption spectrum from 850 to 1800 nm. Our proof-of-principle experiment in a rat burn model illustrates that the combination of multispectral SWIR imaging, SFDI, and unstructured illumination can characterize in vivo changes in skin optical properties over a greatly expanded wavelength range. In the rat burn experiment, these changes (relative to normal, unburned skin) included increased absorption and increased scattering amplitude and slope, consistent with changes that we previously reported in the near-infrared using SFDI.