Quantum-cascade (QC) detectors are photovoltaic infrared detectors that exhibit low-noise characteristics dominated by the Johnson-Nyquist noise owing to the absence of fluctuations brought on by an external operation bias. When the Johnson-Nyquist noise level is low (at high device resistances), the flicker noise cannot be ignored in the lower-frequency region. However, the flicker noise seen in QC detectors has not been sufficiently discussed, and only the Johnson-Nyquist noise has been considered. In this study, we carried out flicker-noise analysis for mid-infrared QC detectors with a response wavelength of approximately 4.5 m using experimental and theoretical approaches. The theoretical predictions, which were based on fluctuating charge-dipoles caused by electron trappings and de-trappings at impurity states, showed qualitative agreement with the measured temperature and device size dependencies of the flicker noise. Because doping of impurities into the absorption well is essential for detector operation, the results suggest that flicker noise is unavoidable in QC detectors. Therefore, to achieve the best low-noise performance of QC detectors, it is important to understand how flicker noise behaves in QC detectors using a theoretical model that considers the experimental results.