Hyperspectral imaging can capture light reflected from tissue with high spectral and spatial resolution. Fitting algorithms can be applied to the spectrum at each pixel to estimate tissue chromophore concentrations, including blood, melanin, water, and fat. Traditional fitting methods are computationally intensive and slow when applied over an entire image. This study developed an artificial neural network (ANN) to rapidly calculate tissue oxygenation, blood, and melanin content from hyperspectral images. Linearly polarized light from a halogen lamp was delivered through a ring illuminator placed 20 cm from the tissue surface. A 1024x1224 pixel hyperspectral camera captured diffusely reflected light through an orthogonal polarizer at 299 wavelengths between 400-1000nm. To train an ANN, diffusion theory was used to generate reflectance spectra from 440-800nm for a uniform tissue containing 24,000 random combinations of physiologically relevant concentrations of oxyhemoglobin, deoxyhemoglobin, melanin, and scattering. The ANN was then tested by generating another 6,000 reflectance spectra from diffusion theory using physiological values and comparing the chromophore concentrations output by the ANN to ground truth values. The ANN demonstrated a root-mean-square error less than 0.01 in predicting each chromophore concentration from reflectance spectra simulated by diffusion theory. An in vivo finger occlusion experiment demonstrated the ability of the system to quantify changes in oxygen saturation and blood volume. This work demonstrates a new deep learning approach to rapidly process hyperspectral image data and accurately quantify tissue components.