The internal electronic structures of single semiconductor nanowires can be resolved using photomodulated Rayleigh scattering spectroscopy. The Rayleigh scattering from semiconductor nanowires is strongly polarization sensitive which allows a nearly background-free method for detecting only the light that is scattered from a single nanowire. While the Rayleigh scattering efficiency from a semiconductor nanowire depends on the dielectric contrast, it is relatively featureless as a function of energy. However, if the nanowire is photomodulated using a second pump laser beam, the internal electronic structure can be resolved with extremely high signal-to-noise and spectral resolution. The photomodulated Rayleigh scattering spectra can be understood theoretically as a first derivative of the scattering efficiency that results from a modulation of the band gap and depends sensitively on the nanowire diameter. Fits to spectral lineshapes provide both the band structure and the diameter of individual GaAs and InP nanowires under investigation.