We investigate the gate field dependence of light absorption and emission of an individual, suspended semiconducting carbon nanotube using Raman and photoluminescence spectroscopies. We find a strong reduction in the absorption strength and a red shift of the E33 state of the nanotube with increasing gate field. The photoluminescence from the E11 state is quenched even stronger. We explain these observations in terms of field-doping and its effects on both the radiative and nonradiative decay rates of the excitons. Thus, gate field-induced doping constitutes an effective means of controlling the optical properties of carbon nanotube devices.