Scale invariant neural dynamics are a relatively new but effective means of measuring changes in brain states as a result of varied cognitive load and task difficulty. This study tests whether scale invariance (as measured by the Hurst exponent, H) can be used with functional near-infrared spectroscopy (fNIRS) to quantify cognitive load, paving the way for scale-invariance to be measured in a variety of real-world settings. We analyzed H extracted from the fNIRS time series while participants completed an N-back working memory task. Consistent with what has been demonstrated in fMRI, the current results showed that scale-invariance analysis significantly differentiated between task and rest periods as calculated from both oxy- (HbO) and deoxy-hemoglobin (HbR) concentration changes. Results from both channel-averaged H and a multivariate partial least squares approach (Task PLS) demonstrated higher H during the 1-back task than the 2-back task. These results were stronger for H derived from HbR than from HbO. This suggests that scale-free brain states are a robust signature of cognitive load and not limited by the specific neuroimaging modality employed. Further, as fNIRS is relatively portable and robust to motion-related artifacts, these preliminary results shed light on the promising future of measuring cognitive load in real life settings.