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Participant movement is a major source of artifacts in functional near-infrared spectroscopy (fNIRS) experiments. Mitigating the impact of motion artifacts (MAs) is crucial to estimate brain activity robustly. Here, we suggest and evaluate a novel application of the nonlinear Hammerstein–Wiener model to estimate and mitigate MAs in fNIRS signals from direct-movement recordings through IMU sensors mounted on the participant’s head (head-IMU) and the fNIRS probe (probe-IMU). To this end, we analyzed the hemodynamic responses of single-channel oxyhemoglobin (HbO) and deoxyhemoglobin (HbR) signals from 17 participants who performed a hand tapping task with different levels of concurrent head movement. Additionally, the tapping task was performed without head movements to estimate the ground-truth brain activation. We compared the performance of our novel approach with the probe-IMU and head-IMU to eight established methods (PCA, tPCA, spline, spline Savitzky–Golay, wavelet, CBSI, RLOESS, and WCBSI) on four quality metrics: SNR, △AUC, RMSE, and R. Our proposed nonlinear Hammerstein–Wiener method achieved the best SNR increase (<i>p</i> < 0.001) among all methods. Visual inspection revealed that our approach mitigated MA contaminations that other techniques could not remove effectively. MA correction quality was comparable with head- and probe-IMUs.