Using an apparatus that images the momentum distribution of individual, isolated 100-nm-scale plasmas, we make the first experimental observation of shock waves in nanoplasmas. We demonstrate that the introduction of a heating pulse prior to the main laser pulse increases the intensity of the shock wave, producing a strong burst of quasimonoenergetic ions with an energy spread of less than 15%. Numerical hydrodynamic calculations confirm the appearance of accelerating shock waves and provide a mechanism for the generation and control of these shock waves. This observation of distinct shock waves in dense plasmas enables the control, study, and exploitation of nanoscale shock phenomena with tabletop-scale lasers.