Children born extremely preterm (EPT) may have difficulties in response inhibition, but the neural basis of such problems is unknown. We recorded magnetoencephalography (MEG) during a somatosensory Go/NoGo task in 6-year-old children born EPT (n = 22) and in children born full term (FT; n = 21). The children received tactile stimuli randomly to their left little (target) and index (non-target) finger and were instructed to squeeze a soft toy with the opposite hand every time they felt a stimulus on the little finger. Behaviorally, the EPT children performed worse than the FT children, both in responding to the target finger stimulation and in refraining from responding to the non-target finger stimulation. In MEG, after the non-target finger stimulation (i.e., during the response inhibition), the sensorimotor alpha oscillation levels in the contralateral-to-squeeze hemisphere were elevated in the FT children when compared with a condition with corresponding stimulation but no task (instead the children were listening to a story and not attending to the fingers). This NoGo task effect was absent in the EPT children. Further, in the sensorimotor cortex contralateral to the tactile stimulation, the post-stimulus suppression was less pronounced in the EPT than FT children. We suggest that the missing NoGo task effect and lower suppression of sensorimotor oscillations are markers of deficient functioning of the sensorimotor networks in the EPT children.