The modulation of the Gilbert damping constant α in (Ga,Mn)As by the application of an electric field is detected by ferromagnetic resonance measurements, where α increases with decreasing hole concentration. The smaller modulation of other magnetic parameters, such as magnetic anisotropy fields and Landé g factor, suggests that the modulation of α is governed by other effects rather than the spin-orbit coupling. Comparison of the conductivity dependence of α with that of the magnetization indicates that the magnetic disorder induced by carrier localization plays a major role in determining the magnitude of α in (Ga,Mn)As.