Commercial hyperspectral imaging systems typically use CCD or CMOS sensors. These types of sensors have a limited dynamic range and non-linear response. This means that when evaluating an artwork under uncontrolled lighting conditions and with light and dark areas in the same scene, hyperspectral images with underexposed or saturated areas would be obtained at low or high exposure times, respectively. To overcome this problem, this article presents a system for capturing hyperspectral images consisting of a matrix of twelve spectral filters placed in twelve cameras, which, after processing these images, makes it possible to obtain the high dynamic range image to measure the spectral reflectance of the work of art being evaluated. We show the developed system and describe all its components, calibration processes, and the algorithm implemented to obtain the high dynamic range spectral reflectance measurement. In order to validate the system, high dynamic range spectral reflectance measurements from Labsphere’s Spectralon Reflectance Standards were performed and compared with the same reflectance measurements but using low dynamic range images. High dynamic range hyperspectral imaging improves the colorimetric accuracy and decreases the uncertainty of the spectral reflectance measurement based on low dynamic range imaging.