The ability to modulate light at high speeds is of paramount importance for telecommunications, information processing, and medical imaging technologies. This has stimulated intense efforts to master optoelectronic switching at visible and near-infrared frequencies, although coping with current computer speeds in integrated architectures still remains a major challenge. As a partial success, midinfrared light modulation has been recently achieved through gating patterned graphene. Here we show that atomically thin noble metal nanoislands can extend optical modulation to the visible and near-infrared spectral range. We find plasmons in thin metal nanodisks to produce similar absorption cross-sections as spherical particles of the same diameter. Using realistic levels of electrical doping, plasmons are shifted by about half their width, thus leading to a factor-of-two change in light absorption. These results, which we substantiate on microscopic quantum theory of the optical response, hold great potential for the development of electrical visible and near-infrared light modulation in integrable, nanoscale devices.