Near-infrared spectroscopy (NIRS) is receiving much attention in the fields of brain-computer interface (BCI) due to its noninvasiveness, usability, and high performance. However, NIRS is susceptible to the motion artifacts, and its high morphological variety hinders the existing signals artifacts elimination techniques from being applied to NIRS. This study proposes a novel feature extraction method for classifying motion artifacts. NIRS data from an open access dataset containing five types of motion artifact (i.e., eye blinking, head movement, eyes movement, teeth clenching, and mouth opening) from 28 healthy subjects were analyzed. The efficacy of the proposed wavelet statistical feature extraction method in artifact classification was compared to various existing feature extraction methods for BCI designs. Each feature was learned by four conventional machine learning models for classifying NIRS motion artifacts. Shrinkage regularized linear discriminant analysis (SRLDA) with the proposed features derived from oxy and deoxy-hemoglobin NIRS signal achieved 90% accuracy and 0.85 Cohen's kappa coefficient for classifying types of motion artifacts. Mann-Whitney U test and paired T-test indicate that SRLDA with the proposed feature had significantly higher classification performance compared to the other models. The proposed method can reliably classify the motion artifacts to standardize the morphology types of NIRS artifact. It could be used to augment signal quality control technique with further extension in future NIRS-based BCI systems.