We report the pressure-dependent optical reflectivity spectra of a strongly correlated insulator, samarium monosulfide (SmS), in the far- and middle-infrared regions to investigate the origin of the pressure-induced phase transition from the black phase to the golden phase. The energy gap becomes narrow with increasing pressure in the black phase. A valence transition from Sm2+ in the black phase to mainly Sm3+ in the golden phase accompanied by spectral change from insulator to metal were observed at the transition pressure of 0.65 GPa. The black-to-golden phase transition occurs when the energy gap size of black SmS becomes the same as the binding energy of the exciton at the indirect energy gap before the gap closes. This result indicates that the valence transition originates from an excitonic instability.