Fano resonances with a characteristic asymmetric line shape can be observed in light scattering, transmission and reflection spectra of resonant optical systems. They result from interference between direct and indirect, resonance-assisted pathways. In the nanophotonics field, Fano effects have been observed in a wide variety of systems, including metallic nanoparticle assemblies, metamaterials and photonic crystals. Their unique properties find extensive use in applications, including optical filtering, polarization selectors, sensing, lasers, modulators and nonlinear optics. We report on the observation of a Fano resonance in a single semiconductor nanostructure, opening up opportunities for their use in active photonic devices. We also show that Fano-resonant semiconductor nanostructures afford the intriguing opportunity to simultaneously measure the far-field scattering response and the near-field energy storage by extracting photogenerated charge. Together they can provide a complete experimental characterization of this type of resonance.