Hemispheric asymmetries have long been seen as characterizing the human brain; yet, an increasing number of reports suggest the presence of such brain asymmetries in our closest primate relatives. However, most available data in non-human primates have so far been acquired as part of neurostructural approaches such as MRI, while comparative data in humans are often dynamically acquired as part of neurofunctional studies. In the present exploratory study in baboons (Papio anubis), we tested whether brain lateralization could be recorded non-invasively using a functional Near-Infrared Spectroscopy (fNIRS) device in two contexts: motor and auditory passive stimulations. Under light propofol anaesthesia monitoring, three adult female baboons were exposed to a series of (1) left- versus right-arm passive movement stimulations; and (2) left- versus right-ear versus stereo auditory stimulations while recording fNIRS signals in the related brain areas (i.e., motor central sulcus and superior temporal cortices respectively). For the sensorimotor condition our results show that left-arm versus right-arm stimulations induced typical contralateral difference in hemispheric activation asymmetries in the three subjects. For the auditory condition, we also revealed typical human-like patterns of hemispheric asymmetries in one subject, namely a leftward lateralization for right ear stimulations for all three channels. Overall, our findings support the use of fNIRS to investigate brain processing in non-human primates from a functional perspective, opening the way for the development of non-invasive procedures in non-human primate brain research.