The cortical motor system can be reorganized following a stroke, with increased recruitment of the contralesional hemisphere. However, it is unknown whether a similar hemispheric shift occurs in the somatosensory system to adapt to this motor change, and whether this is related to movement impairments. This proof-of-concept study assessed somatosensory evoked potentials (SEPs), P50 and N100, in hemiparetic stroke participants and age-matched controls using high-density electroencephalograph (EEG) recordings during tactile finger stimulation. The laterality index was calculated to determine the hemispheric dominance of the SEP and re-confirmed with source localization. The study found that latencies of P50 and N100 were significantly delayed in stroke brains when stimulating the paretic hand. The amplitude of P50 in the contralateral (to stimulated hand) hemisphere was negatively correlated with the Fügl–Meyer upper extremity motor score in stroke. Bilateral cortical responses were detected in stroke, while only contralateral cortical responses were shown in controls, resulting in a significant difference in the laterality index. These results suggested that somatosensory reorganization after stroke involves increased recruitment of ipsilateral cortical regions, especially for the N100 SEP component. This reorganization delays the latency of somatosensory processing after a stroke. This research provided new insights related to the somatosensory reorganization after stroke, which could enrich future hypothesis-driven therapeutic rehabilitation strategies from a sensory or sensory-motor perspective.