Nanoantennas are key optical components for light harvesting; photodiodes convert light into a current of electrons for photodetection. We show that these two distinct, independent functions can be combined into the same structure. Photons coupled into a metallic nanoantenna excite resonant plasmons, which decay into energetic, "hot" electrons injected over a potential barrier at the nanoantenna-semiconductor interface, resulting in a photocurrent. This dual-function structure is a highly compact, wavelength-resonant, and polarization-specific tight detector, with a spectral response extending to energies well below the semiconductor band edge.