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 (p textless 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.