Hyperspectral cameras capture spectral information at each pixel in an image. Acquired spectra can be analyzed to estimate quantities of absorbing and scattering components, but the use of traditional fitting algorithms over megapixel images can be computationally intensive. Deep learning algorithms can be trained to rapidly analyze spectral data and can potentially process hyperspectral camera data in real time. A hyperspectral camera was used to capture wide-field reflectance images of in vivo human tissue at 205 wavelength bands from 420 to 830nm. The optical properties of oxyhemoglobin, deoxyhemoglobin, melanin, and scattering were used with multi-layer Monte Carlo models to generate simulated diffuse reflectance spectra for 24,000 random combinations of physiologically relevant tissue components. These spectra were then used to train an artificial neural network (ANN) to predict tissue component concentrations from an input reflectance spectrum. The ANN achieved low root mean square errors in a test set of 6000 independent simulated diffuse reflectance spectra while calculating concentration values more than 4000× faster than a conventional iterative least squares approach. In vivo finger occlusion and gingival abrasion studies demonstrate the ability of this approach to rapidly generate high-resolution images of tissue component concentrations from a hyperspectral dataset acquired from human subjects.