Plasmonic clusters can exhibit Fano resonances with unique and tunable asymmetric line shapes, which arise due to the coupling of bright and dark plasmon modes within each multiparticle structure. These structures are capable of generating remarkably large local electromagnetic field enhancements and should give rise to high hot carrier yields relative to other plasmonic nanostructures. While the scattering properties of individual plasmonic Fano resonances have been characterized extensively both experimentally and theoretically, their absorption properties, critical for hot carrier generation, have not yet been measured. Here, we utilize single-particle absorption spectroscopy based on photothermal imaging to distinguish between the radiative and nonradiative properties of an individual Fano cluster. In observing the absorption spectrum of individual Fano clusters, we directly verify the theoretical prediction that while Fano interference may be prominent in scattering, it is completely absent in absorption. Our results provide microscopic insight into the nature of Fano interference in systems of coupled plasmonic nanoparticles and should pave the way for the optimization of hot carrier production using plasmonic Fano clusters.