Mid-infrared (IR) array detectors have been used for astronomical observations in space. However, the uniformities of their spectral response curves have not been investigated in detail, the understanding of which is important for spectroscopic observations using large array formats. We characterize the spectral responses of all the pixels in IR array detectors using a Fourier transform infrared spectrometer and cryogenic optics for measurements at high signal-to-noise ratios. We measured the spectral responses of the Si:As impurity band conduction (IBC) array, a flight back-up detector for AKARI/IRC. As a result, we find that the Si:As array has intrinsic variations in the spectral response along the row and column directions of the array. We also find that the cutoff wavelength of the Si:As IBC array depends on the intensity of the incident light.