The gate‐tunable wide‐band absorption of graphene makes it suitable for light modulation from terahertz to visible light. The realization of graphene‐based modulators, however, faces challenges connected with graphene's low absorption and the high electric fields necessary to change graphene's optical conductivity. Here, a solid‐state supercapacitor effect with the high‐k dielectric hafnium oxide is demonstrated that allows modulation from the near‐infrared to shorter wavelengths close to the visible spectrum with remarkably low voltages (≈3 V). The electroabsorption modulators are based on a Fabry–Perot‐resonator geometry that allows modulation depths over 30% for free‐space beams.