Monitoring speech tasks with functional near-infrared spectroscopy (fNIRS) enables investigation of speech production mechanisms and informs treatment strategies for speech-related disorders such as stuttering. Unfortunately, due to movement of the temporalis muscle, speech production can induce relative movement between probe optodes and skin. These movements generate motion artifacts during speech tasks. In practice, spurious hemodynamic responses in functional activation signals arise from lack of information about the consequences of speech-related motion artifacts, as well as from lack of standardized processing procedures for fNIRS signals during speech tasks. To this end, we characterize the effects of speech production on fNIRS signals, and we introduce a systematic analysis to ameliorate motion artifacts. The study measured 50 healthy subjects performing jaw movement (JM) tasks and found that JM produces two different patterns of motion artifacts in fNIRS. To remove these unwanted contributions, we validate a hybrid motion-correction algorithm based sequentially on spline interpolation and then wavelet filtering. We compared performance of the hybrid algorithm with standard algorithms based on spline interpolation only and wavelet decomposition only. The hybrid algorithm corrected 94% of the artifacts produced by JM, and it did not lead to spurious responses in the data. We also validated the hybrid algorithm during a reading task performed under two different conditions: reading aloud and reading silently. For both conditions, we observed significant cortical activation in brain regions related to reading. Moreover, when comparing the two conditions, good agreement of spatial and temporal activation patterns was found only when data were analyzed using the hybrid approach. Overall, the study demonstrates a standardized processing scheme for fNIRS data during speech protocols. The scheme decreases spurious responses and intersubject variability due to motion artifacts.