A droplet placed in a liquid-liquid solution is expected to grow, or shrink, in time as approximately t;{1/2}. In this Letter, we report experimental evidence that when the composition in the interface is far from thermodynamic equilibrium due to the nonideality of the mixture, a droplet shrinks as approximately t. This scaling is due to the coupling between mass and momentum transfer known as Korteweg forces as a result of which the droplet self-propels around. The consequent hydrodynamic convection greatly enhances the mass transfer between the droplet and the bulk phase. Thus, the combined effect of nonideality and nonequilibrium modifies the dynamical behavior of the dissolving droplet.