The detection of motion artifacts in electroencephalogram (EEG) analysis is a high priority, especially for wearable, portable, or wireless EEG monitoring systems. Recently, many scholars have proposed numerous promising techniques to address this issue, e.g., blind source separation (BSS) and independent component analysis (ICA). However, real-time detection with low processing time and friendly use for embedded systems in wearable devices still needs more investigation. Therefore, in this paper, we considered an alternative method for approaching the motion artifact detection problem in EEG signals and proposed a new method called multiscale modified-distribution entropy (M-mDistEn). An efficient coarse-grained procedure was added into the modified-distribution entropy (mDistEn) to consider the various scales (frequencies) of the signals. The results showed that this method is suitable for distinguishing between noisy and normal portions of the signal with a maximum accuracy of approximately 93%. In addition, the M-mDistEn method led to $p$ -values of less than 0.05, indicating statistically significant results of differentiating the motion artifact EEG signals from the clean EEG signals. By comparing the different multiscale entropies, our proposed multiscale entropy was more accurate and robust. Thus, the proposed M-mDistEn method is an effective and efficient entropy method for the analysis of EEG signals corrupted by motion artifacts.