Photodetector nonlinearity, the main limiting factor in terms of optical power in the detection chain, is corrected to improve the signal-to-noise ratio of a short-time measurement in dual-comb spectroscopy. An iterative correction algorithm minimizing out-of-band spectral artifacts based on nonlinearity correction methods used in classical Fourier-transform spectrometers is presented. The exactitude of the nonlinearity correction is validated using a low power linear measurement. Spectroscopic lines of H12CN are provided and the increase in absorption depth of 24% caused by the saturation of the detector is corrected yielding residuals limited by the measurement noise.