Functional near-infrared spectroscopy is prone to contamination by motion artifacts (MAs). Motion correction algorithms have previously been proposed and their respective performance compared for evoked rain activation studies. We study instead the effect of MAs on "oscillation" data which is at the basis of functional connectivity and autoregulation studies. We use as our metric of interest the interhemispheric correlation (IHC), the correlation coefficient between symmetrical time series of oxyhemoglobin oscillations. We show that increased motion content results in a decreased IHC. Using a set of motion-free data on which we add real MAs, we find that the best motion correction approach consists of discarding the segments of MAs following a careful approach to minimize the contamination due to band-pass filtering of data from "bad" segments spreading into adjacent "good" segments. Finally, we compare the IHC in a stroke group and in a healthy group that we artificially contaminated with the MA content of the stroke group, in order to avoid the confounding effect of increased motion incidence in the stroke patients. After motion correction, the IHC remains lower in the stroke group in the frequency band around 0.1 and 0.04 Hz, suggesting a physiological origin for the difference. We emphasize the importance of considering MAs as a confounding factor in oscillation-based functional near-infrared spectroscopy studies.